math on train

8/15/2019 Math on Train

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0 . 8 % $ 1. 0

% $1 0

$3!

$ 2.9 'appro%.)8 12

View Answer Workspace Report Discuss in Forum

. 4f ! a $ 312!* then the -alue of ! ' a 3) is,

A. 2! B. 12!

C. 62! D. 162!

Answer & Explanation

Answer: "ption A

Explanation:

! a $ 312! ! a $ ! !

a $ !.

! ' a 3) $ ! '! 3) $ ! 2 $ 2!.


!. 4f 3 ' x y ) $ 2 and 3 ' x y ) $ 2 3* then x is e7ual to,

A. 0 B. 2

C. D. 6


Answer: "ption C

Explanation:

3 x y $ 2 $ 3 3 x y $ 3 ....'i)

3 x y $ 2 3 $ 3 ! x y $ ! ....'ii)


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"n sol-ing 'i) and 'ii)* +e get x $ .

11. '2 3) n /! % 32n 1

$ ?9 n % 3n 1

A. 1 B. 2

C. 9 D. 3 n


Answer: "ption C

Explanation:

Ki-en =%pression

$'3 ! ) ' n /!) % 32n 1

'3 2) n % 3n 1

$'3 ! % ' n /!) % 32n 1 )

'3 2n % 3n 1)

$'2 3) ' n /!) % 32 n 1

9 n % 3n 1

$3

n

% 32n 1

3 2n % 3n 1

http://www.indiabix.com/aptitude/surds-and-indices/discussion-304http://www.indiabix.com/aptitude/surds-and-indices/discussion-305


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12. 1 1$ ?

1 a ' n m ) 1 a ' m n )

A. 0 B.

1

2

C. 1 D. a m n


Answer: "ption C

Explanation:

1 1 $ 1 1

1 a n

a m

1 a m

a n

1 a ' n m ) 1 a ' m n )

$a m a n

' a m a n) ' a m a n)

$

3 3n 1

3 3n 1

$ 3 '3 n 1 3 n 1) $ 3 2 $ 9.

$3 ' n 2 n 1)

3 '2 n n 1)

$ x ' b c )' b c a ) . x ' c a )' c a b ) . x ' a b )' a b c )

http://www.indiabix.com/aptitude/surds-and-indices/discussion-303


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$' a m a n)

' a m a n)

$ 1.


13. 4f m and n are +hole num ers such that m n $ 121* the -alue of ' m 1) n 1 is,

A. 1 B. 10

C. 121 D. 1000


Answer: "ption D

Explanation:

We kno+ that 11 2 $ 121.

utting m $ 11 and n $ 2* +e get,

' m 1) n 1 $ '11 1) '2 1) $ 10 3 $ 1000.


1 . x b ' b c a ).

x c ' c a b ).

x a ' a b c )

$ ? x c x a x b

A. x abc B. 1

C. x ab bc ca D. x a b c


Answer: "ption B

Explanation:

Ki-en =%p.

http://www.indiabix.com/aptitude/surds-and-indices/discussion-307


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1!.4f x $ 3 22* then the -alue of x

1is,

x

A. 1 B. 2

C. 22 D. 33


Answer: "ption B

$ x ' b c )' b c a ) . x ' c a )' c a b ) . x ' a b )' a b c )

$ x ' b c )' b c ) a ' b c ) . x ' c a )' c a ) b ' c a )

. x ' a b )' a b ) c ' a b )

$ ' x 0 % x 0)

$ x ' b 2 c 2 c 2 a 2 a 2 b 2) . x a ' b c ) b ' c a ) c ' a b )

$ '1 % 1) $ 1.

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Explanation:

x 1 2

$ x 1

2 x x

$ '3 22) 1 2'3 22)

$ '3 22) 1

%'3 22)

2'3 22) '3 22)

$ '3 22) '3 22) 2

$ .

x

1$ 2.

x

PIPE

1. (hree pipes A* @ and D can f ill a tank from e mpt to full in 30 minutes* 20 minutes* and 10minutes respecti-el . When the tank is empt * all the three pipes are opened. A* @ and Ddischarge chemical solutions *F and respecti-el . What is the proportion of the solution in theli7uid in the tank after 3 minutes?

A.

!

11 B.

6

11

C.11

D.

8

11


Answer: "ption B

Explanation:

art filled 'A @ D) in 3 minutes $ 31 1 1

$ 3 %11

$11

.30 20 10 60 20

art filled D in 3 minutes $ 3 .

http://www.indiabix.com/aptitude/pipes-and-cistern/discussion-418http://www.indiabix.com/aptitude/pipes-and-cistern/discussion-418


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10

e7uired ratio $3

%20

$6

.

10 11 11View Answer Workspace Report Discuss in Forum

2. ipes A and @ can fill a tank in ! and 6 hours respecti-el . ipe D can empt it in 12 hours. 4f allthe three pipes are opened together* then the tank +i ll e filled in,

A.1

13hours

1 B.

28

hours11

C.3

9hours

1 D.

1hours

2


Answer: "ption C

Explanation:

et part filled in 1 hour

1 1 1

$

1

.! 6 12 60

(he tank +ill e full in60

hours i.e., 39

hours.1 1


3.A pump can fill a tank +ith +ater in 2 hours. @ecause of a leak* it took 2 hours to fill the tank.(he leak can drain all the +ater of the tank in,

A.

1hours

3 B. hours

C. 8 hours D. 1 hours

http://www.indiabix.com/aptitude/pipes-and-cistern/discussion-429http://www.indiabix.com/aptitude/pipes-and-cistern/discussion-429http://www.indiabix.com/aptitude/pipes-and-cistern/discussion-420http://www.indiabix.com/aptitude/pipes-and-cistern/discussion-429


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Answer: "ption D

Explanation:

Work done the leak in 1 hour $1 3

$1

.2 1

&eak +ill empt the tank in 1 hrs.


.(+o pipes A and @ can fill a cistern in 3 minutes and ! minutes respecti-el . @oth pipes areopened. (he cistern +ill e filled in :ust half an hour* if the @ is turned off after,

A. ! min. B. 9 min.

C. 10 min. D. 1! min.


Answer: "ption B

Explanation:

&et @ e turned off after x minutes. (hen*

art filled 'A @) in x min. art filled A in '30 x ) min. $ 1.

x 2 1

'30 x ).2

$ 1! ! !

11 x '60 2 x )$ 1

22! !

11 x 180 6 x $ 22!.

x $ 9.


!. A tank is filled three pipes +ith uniform flo+. (he first t+o pipes operating simultaneousl fill


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the tank in the same time during +hich the tank is filled the third pipe alone. (he second pipefills the tank ! hours faster than the first pipe and hours slo+er than the third pipe. (he timere7uired the first pipe is,

A. 6 hours B. 10 hours

C. 1! hours D. 30 hours


Answer: "ption C

Explanation:

# up pose* first pipe alone takes x hours to fill the ta nk .

( he n* second and third pipes +ill take ' x !) and ' x 9) hours respecti-el to fill the tank.

1 1$

1

x ' x !) ' x 9)

x ! x $

1

x ' x !) ' x 9)

'2 x !)' x 9) $ x ' x !)

x 2 18 x ! $ 0

' x 1!)' x 3) $ 0

x $ 1!. >neglecting x $ 3

6. (+o pipes can fill a tank in 20 and 2 minutes respecti-el and a +aste pipe can empt 3 gallonsper minute. All the three pipes +orking together can fill the tank in 1! minutes. (he capacit ofthe tank is,

A. 60 gallons B. 100 gallons

C. 120 gallons D. 180 gallons


Answer: "ption C

Explanation:



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Work done the +aste pipe in 1 min ute $1 1 1

1! 20 2

$1 11

1! 120

$ 1

. > -e sign means empt ing0


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x $ 3! hrs.


8. (+o pipes A and @ together can fill a cistern in hours. 5ad the een opened separatel * then @+ould ha-e taken 6 hours more than A to fill the cistern. 5o+ much time +ill e taken A to fillthe cistern separatel ?

A. 1 hour B. 2 hours

C. 6 hours D. 8 hours


Answer: "ption C

Explanation:

&et the cistern e filled pipe A alone in x hours.

(hen* pipe @ +ill fill it in ' x 6) hours.

1 1$

1

x ' x 6)

x 6 x $

1

x ' x 6)

x 2 2 x 2 $ 0

' x 6)' x ) $ 0

x $ 6. >neglecting the negati-e -alue of x


9. (+o pipes A and @ can fill a tank in 20 and 30 minutes respecti-el . 4f oth the pipes are usedtogether* then ho+ long +ill it take to fill the tank?

A. 12 min B. 1! min

C. 2! min D. !0 min



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Answer: "ption A

Explanation:

art filled A in 1 min $1

.20

art filled @ in 1 min $1

.30

art filled 'A @) in 1 min $1 1

$1

.20 30 12

@oth pipes can fill the tank in 12 minutes.


10. (+o pipes A and @ can fill a tank in 1! minutes and 20 minutes respecti-el . @oth the pipes areopened together ut after minutes* pipe A is turned off. What is the total time re7uired to fill thetank?

A. 10 min. 20 sec. B. 11 min. ! sec.

C. 12 min. 30 sec. D. 1 min. 0 sec.Answer & Explanation

Answer: "ption D

Explanation:

1 , 8 :: 1 , x

20 1!



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x $8

% 1 % 20 $ 102

min $ 10 min. 0 sec.1! 3

(he tank +ill e full in ' min. 10 min. 0 sec.) $ 1 min. 0 sec.

11. "ne pipe can fill a tank three times as fast as another pipe. 4f together the t+o pipes can fill thetank in 36 minutes* then the slo+er pipe alone +ill e a le to fill the tank in,

A. 81 min. B. 108 min.

C. 1 min. D. 192 min.


Answer: "ption C

Explanation:

&et the slo+er pipe alone fill the tank in x minutes.

(hen* faster pipe +ill fill it in x

minutes.3

1 3$

1

x x 36

$1

x 36

x $ 1 min.


12. A large tanker can e filled t+o pipes A and @ in 60 minutes and 0 minutes respecti-el . 5o+man minutes +ill it take to fill the tanker from empt state if @ is used for half the time and Aand @ fill it together for the other half?

A. 1! min B. 20 min

C. 2 .! min D. 30 min




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Answer: "ption D

Explanation:

art filled 'A @) in 1 minute $1 1

$1

.60 0 2

#uppose the tank is filled in x minutes.

(hen* x 1 1

$ 12 2 0

x %

1$ 1

2 1!

x $ 30 min.


13. A tap can fill a tank in 6 hours. After half the tank is filled* three more similar taps are opened.What is the total time taken to fill the tank completel ?

A. 3 hrs 1! min B. 3 hrs ! min

C. hrs D. hrs 1! min


Answer: "ption B

Explanation:

(ime taken one tap to fill half of the tank $ 3 hrs.

art filled the four taps in 1 hour $ %1

$2

.6 3

emaining part $ 1 1

$1

.2 2

2,

1:: 1 , x

3 2



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x $1

% 1 %3

$3

hours i.e., ! mins.2 2

#o* total time taken $ 3 hrs. ! mins.


1 . (hree taps A* @ and D can fill a tank in 12* 1! and 20 hours respecti-el . 4f A is open all the timeand @ and D are open for one hour each alternatel * the tank +ill e full in,

A. 6 hours B.6

2hours

3

C. hours D.

1

hours2


Answer: "ption C

Explanation:

'A @)Bs 1 hourBs +ork $1 1

$9

$3

.12 1! 60 20

'A D)Bs hourBs +ork $1 1

$8

$2

.12 20 60 1!

art filled in 2 hrs $3 2

$1

.20 1! 60

art filled in 6 hrs $ 3 %1

$1

.60 20

emaining part $ 1 1

$3

.20 20

o+* it is the turn of A and @ and3

part is filled A and @ in 1 hour.20

(otal time taken to fill the tank $ '6 1) hrs $ hrs.


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1!. (hree pipes A* @ and D can fill a tank in 6 hours. After +orking at it together for 2 hours* D isclosed and A and @ can fill the remaining part in hours. (he num er of hours taken D alone to

fill the tank is,

A. 10 B. 12

C. 1 D. 16


Answer: "ption C

Explanation:

art filled in 2 hours $2

$1

6 3

emaining part $ 1 1

$2

.3 3

'A @)Bs hou rBs +ork $2

3

'A @)Bs 1 hourBs +ork $

2

21

DBs 1 hourBs +ork $ R 'A @ D)Bs 1 hourBs +ork S R 'A @)Bs 1 hourBs +ork S

$1 2

$1

6 21 1

D alone can fill the tank in 1 hours.

PROBABILITY

1. (ickets num ered 1 to 20 are mi%ed up and then a ticket is dra+n at random. What is thepro a ilit that the ticket dra+n has a num er +hich is a multiple of 3 or !?

http://www.indiabix.com/aptitude/probability/discussion-692


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A.

1

2 B.

2

!

C.

8

1! D.

9

20


Answer: "ption D

Explanation:

5ere* # $ R1* 2* 3* * ....* 19* 20S.

&et = $ e-ent of getting a multiple of 3 or ! $ R3* 6 * 9* 12* 1!* 18* !* 10* 20S.

'=) $n '=)

$9

.n '#) 20


2. A ag contains 2 red* 3 green and 2 lue alls. (+o alls are dra+n at random. What is thepro a ilit that none of the alls dra+n is lue?

A.

10

21 B.

11

21

C.

2

D.

!

Ans wer & Explanation

Answer: "ption A

Explanation:

(otal num er of alls $ '2 3 2) $ .

&et # e the sample space.

(hen* n '#) $ um er of +a s of dra+ing 2 alls out of



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$ D2 T

$' % 6)

'2 % 1)

$ 21.

&et = $ =-ent of dra+ing 2 alls* none of +hich is lue.

n '=) $ um er of +a s of dra+ing 2 alls out of '2 3) alls.

$ ! D2

$'! % )

'2 % 1)

$ 10.

'=) $n '=)

$10

.n '#) 21


3. 4n a o%* there are 8 red* lue and 6 green alls. "ne all is picked up randoml . What is thepro a ilit that it is neither red nor green?

A.

1

3 B.

3

C.

19

D.

8

21

E.

9

21


http://www.indiabix.com/aptitude/probability/discussion-701http://www.indiabix.com/aptitude/probability/discussion-690


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Answer: "ption A

Explanation:

(otal num er of alls $ '8 6) $ 21.

&et = $ e-ent that the all dra+n is neither red nor green

$ e-ent that the all dra+n is lue.

n '=) $ .

'=) $n '=)

$ $1

.n '#) 21 3


. What is the pro a ilit of getting a sum 9 from t+o thro+s of a dice?

A.

1

6 B.

1

8

C.

1

9 D.

1

12


Answer: "ption C

Explanation:

4n t+o thro+s of a die* n '#) $ '6 % 6) $ 36.

&et = $ e-ent of getting a sum $R'3* 6)* ' * !)* '!* )* '6* 3)S.

'=) $n '=)

$ $1

.n '#) 36 9


!. (hree un iased coins are tossed. What is the pro a ilit of getting at most t+o heads?


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A.

3

B.

1

C.

3

8 D.

8


Ans wer: "ption D

Explanation:

5ere # $ R(((* ((5* (5(* 5((* (55* 5(5* 55(* 555S

&et = $ e-ent of getting at most t+o heads.

(hen = $ R(((* ((5* (5(* 5((* (55* 5(5* 55(S.

'=) $n '=)

$ .n '#) 8

6. (+o dice are thro+n simultaneousl . What is the pro a ilit of getting t+o num ers +hose productis e-en?

A.

1

2 B.

3

C.

3

8 D.

!

16


Answer: "ption B

Explanation:

4n a simultaneous thro+ of t+o dice* +e ha-e n '#) $ '6 % 6) $ 36.

(hen* = $ R'1* 2)* '1* )* '1* 6)* '2* 1)* '2* 2)* '2* 3)* '2* )* '2* !)* '2* 6)* '3* 2)* '3* )* '3* 6)* ' * 1)* ' * 2)* ' * 3)* ' * )* ' * !)* ' * 6)* '!* 2)* '!* )* '!* 6)* '6* 1)*



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'6* 2)* '6* 3)* ' 6* )* '6* !)* '6* 6)S

n '=) $ 2 .

'=) $

n '=)

$

2

$

3

.n '#) 36


. 4n a class* there are 1! o s and 10 girls. (hree st ude nts are selected at random. (he pro a ilitthat 1 girl and 2 o s are selected* is,

A.

21

6 B.

2!

11

C.

1

!0 D.

3

2!


Answer: "ption A

Explanation:

&et # e the sample space and = e the e-ent of selecting 1 girl and 2 o s.

(hen* n '#) $ um er +a s of selecting 3 students out of 2!

$ 2! D3 T

$'2! % 2 % 23)

'3 % 2 % 1)

$ 2300.

n '=) $ ' 10 D1 % 1! D2)

$ 10 % '1! % 1 )

'2 % 1)

http://www.indiabix.com/aptitude/probability/discussion-702http://www.indiabix.com/aptitude/probability/discussion-702http://www.indiabix.com/aptitude/probability/discussion-693


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$ 10!0.

n '=) 10!0 21

n '#) 2300 6


8. 4n a lotter * there are 10 priLes and 2! lanks. A lotter is dra+n at random. What is thepro a ilit of getting a priLe?

A.

1

10 B.

2

!

C.

2

D.

!


Answer: "ption C

Explanation:

'getting a priLe) $10

$10

$2

.'10 2!) 3!


9. ;rom a pack of !2 cards* t+o cards are dra+n together at random. What is the pro a ilit of oththe cards eing kings?

A.

1

1! B.

2!

!

C.

3!

2!6 D.

1

221

http://www.indiabix.com/aptitude/probability/discussion-696http://www.indiabix.com/aptitude/probability/discussion-696http://www.indiabix.com/aptitude/probability/discussion-696


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Answer: "ption D

Exp lanation:


(hen* n '#) $ !2 D2 $'!2 % !1)

$ 1326.'2 % 1)

&et = $ e-ent of getting 2 kings out of .

n '=) $ D2 $' % 3)

$ 6.'2 % 1)

'=) $n '=)

$6

$1

.n '#) 1326 221


10. (+o dice are tossed. (he pro a ilit that the total score is a prime num er is,

A.

1

6 B.

!

12

C.

1

2 D.

9


Answer: "ption B

Explanation:

Dlearl * n '#) $ '6 % 6) $ 36.

&et = $ =-ent that the sum is a prime num er.

(hen = $ R '1* 1)* '1* 2)* '1* )* '1* 6)* '2* 1)* '2* 3)* '2* !)* '3* 2)* '3* )* ' * 1)* ' * 3)* '!* 2)* '!* 6)* '6* 1)* '6* !) S



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n '=) $ 1!.

'=) $n '=)

$1!

$!

.n '#) 36 12

11. A card is dra+n from a pack of !2 cards. (he pro a ilit of getting a 7ueen of clu or a king ofheart is,

A.

1

13 B.

2

13

C.

1

26 D.

1

!2


Answer: "ption C

Explanation:

5ere* n '#) $ !2.

&et = $ e-ent of getting a 7ueen of clu or a king of heart.

(hen* n '=) $ 2.

'=) $ n '=) $2

$1

.n '#) !2 26


12. A ag contains +hite* ! red and 6 lue alls. (hree alls are dra+n at random from the ag. (hepro a ilit that all of them are red* is,

A.

1

22 B.

3

22

C.

2

91 D.

2




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Answer: "ption C

Explanation:


(hen* n '#) $ num er of +a s of dra+ing 3 alls out of 1!

$ 1! D3

$'1! % 1 % 13)

'3 % 2 % 1)

$ !!.

&et = $ e-ent of getting all the 3 red alls.

n '=) $ ! D3 $ ! D2 $'! % )

$ 10.'2 % 1)

'=) $n '=)

$10

$2

.n '#) !! 91


13. (+o cards are dra+n together from a pack of !2 cards. (he pro a ilit that one is a spade andone is a heart* is,

A.

3

20 B.

29

3

C.100

D.

13

102


Answer: "ption D

Explanation:

http://www.indiabix.com/aptitude/probability/discussion-697http://www.indiabix.com/aptitude/probability/discussion-694


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(hen* n '#) $ !2 D2 $'!2 % !1)

$ 1326.'2 % 1)

&et = $ e-ent of getting 1 spade and 1 heart.

n '=) $ num er of +a s of choosing 1 spade out of 13 and 1 heart out of 13

$ ' 13 D1 % 13 D1)

$ '13 % 13)

$ 169.

'=) $n '=)

$169

$13

.n '#) 1326 102


1 . "ne card is dra+n at random from a pack of !2 cards. What is the pro a ilit that the card dra+nis a face card 'Qack* Fueen and Jing onl )?

A.

1

13 B.

3

13

C.

1

D.

9

!2


Answer: "ption B

Explanation:

Dlearl * there are !2 cards* out of +hich there are 12 face cards.

'getting a face card) $12

$3

.!2 13


$ s. 1600 % 1

! 2

1600 % 1

!

2 % 100 2 % 100


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1!. A ag contains 6 lack and 8 +hite alls. "ne all is dra+n at random. What is the pro a ilit thatthe all dra+n is +hite?

A.

3

B.

C.

1

8 D.

3


Answer: "ption B

Explanation:

&et num er of alls $ '6 8) $ 1 .

um er of +hite alls $ 8.

'dra+ing a +hite all) $8

$ .1

COMPOUND INTEREST

1. A ank offers !E compound interest calculated on half earl asis. A customer deposits s. 1600each on 1 st Qanuar and 1 st Qul of a ear. At the end of the ear* the amount he +ould ha-egained +a of interest is,

A. s. 120 B. s. 121

C. s. 122 D. s. 123


Answer: "ption B

Explanation:

Amount

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205/280

$ s. 3321.

D.4. $ s. '3321 3200) $ s. 121


2. (he difference et+een simple and compound interests compounded annuall on a certain sum ofmone for 2 ears at E per annum is e. 1. (he sum 'in s.) is,

A. 62! B. 630

C. 6 0 D. 6!0


$ s. 1600 % 1 ! 2

1600 % 1 !

2 % 100 2 % 100

$ s. 1600 %

1 1

1

0 0

$ s. 1600 %1

%1

1600% 1

0 0 0

$ s.1600 % 1 % 81

0 % 0



206/280

Answer: "ption A

Explanation:

&et the sum e s. x . (hen*

D.4. $ x 1 2

x $6 6

x x $!1

x .100 62! 62!

#.4. $ x % % 2

$2 x

.100 2!

!1 x 2 x $ 1

62! 2!

x $ 62!.


3. (here is 60E increase in an amount in 6 ears at simple interest. What +ill e the compoundinterest of s. 12*000 after 3 ears at the same rate?

A. s. 2160 B. s. 3120

C. s. 39 2 D. s. 62 0

E. one of these


Answer: "ption C

Explanation:

&et $ s. 100. (hen* #.4. s. 60 and ( $ 6 ears.

$ 100 % 60 $ 10E p.a.

100 % 6

o+* $ s. 12000. ( $ 3 ears and $ 10E p.a.

D.4.

$ s. 12000 % 1 10 3 1

$ s. !000 % 1 % 1 %

100 100

$ s. !000 %26

%!1

2! !0



207/280

100

$ 39 2.


.What is the difference et+een the compound interests on s. !000 for 1 ears at E perannum compounded earl and half earl ?

A. s. 2.0 B. s. 3.06

C. s. .80 D. s. 8.30


Ans wer: "ption A

Explanation:

D.4. +hen interestcompounded earl

$ s. 12000 %331

1000

$ s. !000 % 1 % 1 %

100 100



208/280

$ s. !30 .

D.4. +hen interest iscom pounded half earl

$ s. !306.0

ifference $ s. '!306.0 !30 ) $ s. 2.0


!. (he compound interest on s. 30*000 at E per annum is s. 3 . (he period 'in ears) is,

A. 2 B.2

1

2

C. 3 D.


$ s. !000 %26

%!1

2! !0

$ s.!000 % 1 2 3

100

$ s. !000 % !1 % !1 % !1

!0 !0 !0



209/280

Ans wer: "ption A

Explanation:

Amount $ s. '30000 3 ) $ s. 3 3 .

&et the time e n ears.

(hen* 30000 1 n

$ 3 3100

10 n$

3 3$

11 9$

10 2

100 30000 10000 100

n $ 2 ears.

6. What +ill e the compound interest on a sum of s. 2!*000 after 3 ears at the rate of 12p.c.p.a.?

A. s. 9000.30 B. s. 9 20

C. s. 10123.20 D. s. 10 83.20

E. one of these


Answer: "ption C

Explanation:

Amount

$ s. 2!000 % 1 12 3

100

$ s. 2!000 %28

%28

%28

2! 2! 2!



210/280

$ s. 3!123.20

D.4. $ s. '3!123.20 2!000) $ s. 10123.20


. At +hat rate of compound interest per annum +ill a sum of s. 1200 ecome s. 13 8.32 in 2ears?

A. 6E B. 6.!E

C. E D. .!E


Answer: "ption A

Explanation:

&et the rate e E p.a.

(hen* 1200 % 1 2 $ 13 8.32

100

1 2 $ 13 832 $ 11236

100 120000 10000

1 2 $ 106 2

100 100

1 $ 106

100 100

$ 6E


8. (he least num er of complete ears in +hich a sum of mone put out at 20E compound interest+ill e more than dou led is,

A. 3 B.

$ s. 8000 % 1 ! 2

100

$ s. 8000 %21

%21

20 20

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C. ! D. 6


Answer: "ption B

Explanation:

1 20 n

P 26 n

P 2.100 !

o+*6

%6

%6

%6

P 2.! ! ! !

#o* n $ ears.


10. (he effecti-e annual rate of interest corresponding to a nominal rate of 6E per annum pa a le

$ s. 8000 % 1 ! 2

100

$ s. 8000 % 21 % 21

20 20


212/280

half earl is,

A. 6.06E B. 6.0 E

C. 6.08E D. 6.09E


Answer: "ption D

Explanation:

Amo unt of s. 100 for 1 ear+hen compounded half earl

$ s. 100 % 1 3 2

$ s. 106.09100

=ffecti-e rate $ '106.09 100)E $ 6.09E

11. #imple interest on a certain sum of mone for 3 ears at 8E per annum is half the compoundinterest on s. 000 for 2 ears at 10E per annum. (he sum placed on simple interest is,

A. s. 1!!0 B. s. 16!0

C. s. 1 !0 D. s. 2000


Answer: "ption C

Explanation:

D.4.

$ s. 8 0.

$ s. 000 %11

%11

000

10 10

$ s. 000 % 1 10 2 000

100

$ s. !00 % 1 ! 2

100

$ s. !00 %21

%21

20 20

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#um $ s.20 % 100 $ s. 1 !0.

3 % 8


12. 4f the simple interest on a sum of mone for 2 ears at !E per annum is s. !0* +hat is thecom pound interest on the same at the same rate and for the same time?

A. s. !1.2! B. s. !2

C. s. ! .2! D. s. 60


Answer: "ption A

Explanation:

#um $ s.!0 % 100

$ s. !00.2 % !

Amount

$ s. !!1.2!

D.4. $ s. '!!1.2! !00) $ s. !1.2!


$ s. !00 % 1 ! 2

100

$ s. !00 %21

%21

20 20



214/280

13. (he difference et+een simple interest and compound on s. 1200 for one ear at 10E perannum reckoned half earl is,

A. s. 2.!0 B. s. 3

C. s. 3. ! D. s.

E. one of these


Answer: "ption B

Explanation:

#.4. $ s1200 % 10 % 1

$ s. 120.100

D.4. $ s. 1200 % 1 ! 2

1200 $ s. 123.100

ifference $ s. '123 120) $ s. 3.


1 . (he difference et+een compound interest and simple interest on an amount of s. 1!*000 for 2ears is s. 96. What is the rate of interest per annum?

A. 8 B. 10

C. 12 D. Dannot e determined

E. one of these


Answer: "ption A

Explanation:

1!000 % 1 2

1!0001!000 % % 2

$ 96100 100



215/280

1!000 1 2

1 2

$ 96100 100

1!000'100 ) 2 10000 '200 % )

$ 96

10000

2 $96 % 2

$ 63

$ 8.

ate $ 8E.


1!. (he compound interest on a certain sum for 2 ears at 10E per annum is s. !2!. (he simpleinterest on the same sum for dou le the time at half the rate percent per annum is,

A. s. 00 B. s. !00

C. s. 600 D. s. 800


Answer: "ption B

Explanation:

&et the sum e s. .

#um $ s . 2!00.

#o* #.4. $ s. 2!00 % ! % $ s. !00

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100

PERCENTAGES

1. A atsman scored 110 runs +hich included 3 oundaries and 8 si%es. What percent of his totalscore did he make running et+een the +ickets?

A. !E B.!

!E

11

C.!

6E

11 D. !!E


Answer: "ption B

Exp lanation:

um er of runs made running $ 110 '3 % 8 % 6)

$ 110 '60)

$ !0.

e7uired percentage $!0

% 100E $ !

!E

110 11


2. (+o students appeared at an e%amination. "ne of them secured 9 marks more than the other andhis marks +as !6E of the sum of their marks. (he marks o tained them are,

A. 39* 30 B. 1* 32

C. 2* 33 D. 3* 3


Answer: "ption C

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Exp lanation:

&et their marks e ' x 9) and x .

(hen* x 9 $!6

' x 9 x )100

2!' x 9) $ 1 '2 x 9)

3 x $ 99

x $ 33

#o* their marks are 2 and 33.


3. A fruit seller had some apples. 5e sells 0E apples and still has 20 apples. "riginall * he had,

A. !88 apples B. 600 apples

C. 6 2 apples D. 00 apples


Ans wer: "ption D

Exp lanation:

#uppose originall he h ad x apples.

(hen* '100 0)E of x $ 20.

60% x $ 20

100

x $20 % 100

$ 00.60


. Wha t percentage of num ers from 1 to 0 ha-e 1 or 9 in the unitBs digit?



218/280

A. 1 B. 1

C. 20 D. 21


Answer: "ption C

Explanation:

Dlearl * the num ers +hich ha-e 1 or 9 in the unitBs digit* ha-e s7uares that end in the digit 1.#uch num ers from 1 to 0 are 1* 9* 11* 19* 21* 29* 31* 39* 1* 9* !1* !9* 61* 69.

um er of such num er $1

e7uired percentage $1

% 100

E $ 20E.0


!. 4f A $ x E of y and @ $ y E of x * then +hich of the follo+ing is true?

A. A is smaller than @. B. A is greater than @

C.elationship et+een A and @ cannote determined.

D.4f x is smaller than y * then A is greaterthan @.

E. one of these


Answer: "ption E

Explanation:

x E of y $ x

%y $y

% x $ y E of x 100 100

A $ @.

6. 4f 20E of a $ b * then b E of 20 is the same as,

A. E of a B. !E of a



219/280

C. 20E of a D. one of these


Answer: "ption A

Explanation:

20E of a $ b 20

a $ b .100

b E of 20 $b

% 20 $20

a %1

% 20 $ a $ E of a .100 100 100 100


. 4n a certain school* 20E of students are elo+ 8 ears of age. (he num er of students a o-e 8

ears of age is of the num er of students of 8 ears of age +hich is 8. What is the totalnum er of students in the school?

A. 2 B. 80

C. 120 D. 1!0

E. 100


Answer: "ption E

Explanation:

&et the num er of students e x . (hen*

um er of students a o-e 8 ears of age $ '100 20)E of x $ 80E of x .

80E of x $ 8 2

of 83

80 x $ 80

100

x $ 100.

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8. (+o num ers A and @ are such that the sum of !E of A and E of @ is t+o third of the sum of6E of A and 8E of @. ; ind the ratio of A , @.

A. 2 , 3 B. 1 , 1

C. 3 , D. , 3


Answer: "ption D

Explanation:

!E of A E of @ $2

'6E of A 8E of @)3

! A @ $

2 6 A

8 @

100 100 3 100 100

1 A

1 @ $

1 A @

20 2! 2! !

1 1

A $

1

@20 2! ! 2!

1 A $

1 @

100 !

A$

100$ .

@ ! 3

e7uired ratio $ , 3


9.A student multiplied a num er

3instead of

!.

! 3

What is the percentage error in the calculation?



221/280

A. 3 E B. E

C. ! E D. 6 E


Answer: "ption D

Explanation:

&et the num er e x .

(hen* error $!

x 3

x $16

x .3 ! 1!

=rrorE $16 x

%3

% 100E $ 6 E.1! ! x


10. 4n an election et+een t+o candidates* one got !!E of the total -alid -otes* 20E of the -otes+ere in-alid. 4f the total num er of -otes +as !00* the num er of -alid -otes that the othercandidate got* +as,

A. 2 00 B . 2900

C. 3000 D. 3100


Answer: "ption A

Explanation:

um er of -alid -otes $ 80E of !00 $ 6000.


222/280

11. (hree candidates contested an election and recei-ed 1136* 636 and 11628 -otes respecti-el .What percentage of the total -otes did the +inning candidate get?

A. ! E B. 60E

C. 6!E D. 90E


Answer: "ption A

Exp lanation:

( ota l num er of -otes polled $ '1136 636 1 16 28) $ 20 00.

e7uired percentage $11628

% 100

E $ ! E.20 00


12. (+o tailors H and I are paid a total of s. !!0 per +eek their emplo er. 4f H is paid 120percent of the sum paid to I* ho+ much is I paid per +eek?

A. s. 200 B. s. 2!0

C. s. 300 D. one of these


Answer: "ption B

Explanation:

&et the sum paid to I per +eek e s. % .

(hen* % 120E of % $ !!0.

%

120

% $ !!0100

11 % $ !!0

!

% $ !!0 % !

$ 2!0.11

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Kauri +ent to the stationers and ought things +orth s. 2!* out of +hich 30 paise +ent onsales ta% on ta%a le purchases. 4f the ta% rate +as 6E* then +hat +as the cost of the ta% freeitems?

A. s. 1! B. s. 1!. 0

C. s. 19. 0 D. s. 20


Answer: "ption C

Explanation:

&et the amount ta%a le purchases e s. x .

30

100

30 100

100 6

Dost of ta% free items $ s. >2! '! 0.30) $ s. 19. 0


1 . a:ee- u s good +orth s. 66!0. 5e gets a re ate of 6E on it. After getting the re ate* hepa s sales ta% 10E. ;ind the amount he +ill ha-e to pa for the goods.

A. s. 68 6.10 B. s. 6999.20

C. s. 66! D. s. 000


An swer: "ption A

Explanation:



224/280

e ate $ 6E of s. 66!0 $ s.6

% 66!0 $ s. 399.100

#ales ta% $ 10E of s. '66!0 399) $ s.10

% 62!1 $ s. 62!.10

100 ;inal amount $ s. '62 !1 62!.10) $ s. 68 6.10


1!. (he population of a to+n increased from 1* !*000 to 2*62*!00 in a decade. (he a-erage percentincrease of population per ear is,

A. .3 E B. !E

C. 6E D. 8. !E


Answer: "ption B

Explanation:

4ncrease in 10 ears $ '262!00 1 !000) $ 8 !00.

4ncreaseE $

8 !00

% 100 E $ !0E.1 !000

e7uired a-erage $!0

E $ !E.10

CLOCK 1. An accurate clock sho+s 8 oBclock in the morning. (hrough ho+ ma degrees +ill the hour hand

rotate +hen the clock sho+s 2 oBclock in the afternoon?

A. 1 U B. 1!0U

C. 168U D. 180U


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Answer: "ption D

Explanation:

Angle traced the hour hand in 6 hours $360

% 6U

$ 180U.12


2. (he refle% angle et+een the hands of a clock at 10.2! is,

A. 180U B.192

1 U

2

C. 19!U D.19

1 U

2


Answer: "ption D

Explanation:

Angle traced hour hand in12!

hrs $360

%12! U

$ 3121 U

.

12 12 12 2

Angle traced minute hand in 2! min $360

% 2!U

$ 1!0U.60

efle% angle $ 360U 3121

1!0U

$ 360U 1621 U

$ 191

.2 2 2


3. A clock is started at noon. @ 10 minutes past !* the hour hand has turned through,

A. 1 !U B. 1!0U

C. 1!!U D. 160U


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Answer: "ption C

Explanation:

Angle traced hour hand in 12 hrs $ 360U.

Angle traced hour hand in ! hrs 10 min. i.e.,31

hrs $360

%31 U

$ 1!!U.6 12 6


. A +atch +hich gains ! seconds in 3 minutes +as set right at a.m. 4n the afternoon of the sameda * +hen the +atch indicated 7uarter past oBclock* the true time is,

A. !9 min. past 312

B. p.m.

C.!8 min. past 3

11 D.

23

min. past 11


Answer: "ption B

Explanation:

(ime from a.m. to .1! p.m. $ 9 hrs 1! min. $3

hrs.

3 min. ! sec. of this clock $ 3 min. of the correct clock.

3hrs of this clock $

1hrs of the correct clock.

20 2 0

3hrs of this clock $

1%

20%

3hrs of the correct clock.

20 3

$ 9 hrs of the correct clock.

(he correct time is 9 hrs after a.m. i.e., p.m.



227/280

!. 5o+ much does a +atch lose per da * if its hands coincide e-er 6 minutes?

A.32

8min.

11 B.36

!min.

11

C. 90 min. D. 96 min.


Answer: "ption A

Explanation:

!! min. spaces are co-ered in 60 min.

60 min. spaces are co-ered in60

% 60min.

$ 6!!

min.!! 11

&oss in 6 min. $ 6!!

6 $16

min.11 11

&oss in 2 hrs $16

%1

% 2 % 60min.

$ 328

min.11 6 11

6. At +hat time et+een and 8 oBclock +ill the hands of a clock e in the same straight line ut*not together?

A. ! min. past B.!

2min. past

11

C.!

3min. past

11 D.

!!

min. past 11


Answer: "ption D

Explanation:

When the hands of the clock are in the same straight line ut not together* the are 30 minutespaces apart.

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At oBclock* the are 2! min. spaces apart.

Ginute hand +ill ha-e to gain onl ! min. spaces.

! ! min. spaces are gained in 60 min.

! min. spaces are gained in60

% !min

$ !!

min.!! 11

e7uired time $ !!

min. past .11


. At +hat time et+een !.30 and 6 +ill the hands of a clock e at right angles?

A.3

!min. past !

11 B.

3 min. past !11

C. 0 min. past ! D. ! min. past !


Answer: "ption B

Explanation:

At ! oBclock* the hands are 2! min. spaces apart.

( o e at right angles and that too et+een !.30 a nd 6* the minute hand has to gain '2! 1!)$ 0 min. spaces.

!! min. spaces are gained in 60 min.

0 min. spaces are gained in60

% 0min

$ 3 min.!! 11

e7uired time $ 3 min. past !.11


8. (he angle et+een the minute hand and the hour hand of a clock +hen the time is .20* is,

http://www.indiabix.com/aptitude/clock/discussion-644


229/280

A. 0U B. 10U

C. !U D. 20U


Answer: "ption B

Explanation:

Angle traced hour hand in13

hrs $360

%13 U

$ 130U.3 12 3

Angle traced min. hand in 20 min. $360

% 20U

$ 120U.60

e7uired angle $ '130 120)U $ 10U.


9. At +hat angle the hands of a clock are inclined at 1! minutes past !?

A.!8

1 U

2 B. 6 U

C.6

1 U

2 D.

21 U

2

An sw er & Explanation

An sw er: "ption C

Explanation:


hrs $360

%21 U

$ 1!1 U

12 2

Angle traced min. hand in 1! min. $360

% 1!U

$ 90U.60



230/280

e7uired angle $ 1!1 U

90U $ 61 U

2 2


10. At 3, 0* the hour hand and the minute hand of a clock form an angle of,

A. 120V B. 12!V

C. 130V D. 13!V


Answer: "ption C

Explanation:

Angle traced hour hand in 12 hrs. $ 360V.

Angle traced it in11

hrs $360

%11 V

$ 110V.3 12 3

Angle traced minute ha nd in 60 min. $ 360V.

Angle traced it in 0 min. $360

% 0V

$ 2 0V.

60 e7uired angle '2 0 110)V $ 130V.

11. 5 o+ man times are the hands of a clock at rig ht a ngle in a da ?

A. 22 B. 2

C. D. 8


Answer: "ption C

Explanation:

4n 12 hours* the are at right angles 22 times.

4n 2 hours* the are at right angles times.

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12. (he angle et+een the minute hand and the hour hand of a clock +hen the time is 8.30* is,

A. 80U B. !U

C. 60U D. 10!U


Answer: "ption B

Explanation:


hrs $360

%1 U

$ 2!!.2 12 2

Angle traced min. hand in 30 min. $360

% 30U

$ 180.60

e7uired angle $ '2!! 180)U $ !U.


13. 5o+ man times in a da * are the hands of a clock in straight line ut opposite in direction?

A. 20 B. 22

C. 2 D. 8


Answer: "ption B

Exp lanation:

(he hands of a clock po int in opposite directions 'in the same straight line) 11 times in e-er 12hours. '@ecause et+een ! and the point in opposite directions at 6 oBclcok onl ).

#o* in a da * the hands point in the opposite directions 22 times.




232/280

1 . At +hat time et+een and ! oBclock +ill the hands of a +atch point in opposite directions?

A. ! min. past B. 0 min. past

C. !0 min. past 11

D. !

6

min. past 11


Answer: "ption D

Explanation:

At oBclock* the hands of the +atch are 20 min. spaces apart.

(o e in opposite directions* the must e 30 min. spaces apart.

Ginute hand +ill ha-e to gain !0 min. spaces.

!! min. spaces are gained in 60 min.

!0 min. spaces are gained in60

% !0min. or !

6min.

!! 11

e7uired time $ !6

min. past .11


1!. At +hat time et+een 9 and 10 oBclock +ill the hands of a +atch e together?

A. ! min. past 9 B. !0 min. past 9

C.9

1min. past 9

11 D.

82

min. past 911


Answer: "ption C

Exp lanation:

( o e together et+een 9 and 10 oBclock* the minu te hand has to gain ! min. spaces.



233/280

!! min. spaces gained i n 60 min.

! min. spaces are gained in60

% !min or 9

1min.

!! 11

(he hands are together at 9 1 min. past 9.11

16. At +hat time* in minutes* et+een 3 oBclock and oBclock* oth the needles +ill coincide eachother?

A.!

1 '

11 B.

12 '

11

C. 13 '

11 D. 16

'

11


Answer: "ption D

Explanation:

At 3 oBclock* the minute hand is 1! min. spaces apart from the hour hand.

(o e coincident* it must gain 1! min. spaces.

!! min. are gained in 60 min.

1! min. are gained in60

% 1!min

$ 16 min.!! 11

(he hands are coincident at 16 min. past 3.11


1 . 5o+ man times do the hands of a clock coincide in a da ?

A. 20 B. 21

C. 22 D. 2



234/280


Answer: "ption C

Explanation:

(he hands of a clock coincide 11 times in e-er 12 hours '#ince et+een 11 and 1* the coincideonl once* i.e., at 12 oBclock).

A,

12,001,0!2,113,16

,22!,26,33

,388 ,9, 910,!!

2,

12,001,0!2,113,16

,22!,26,33

,388,9, 910,!!

(he hands o-erlap a out e-er 6! minutes* not e-er 60 minutes.

(he hands coincide 22 times in a da .


18. 5o+ man times in a da * the hands of a clock are straight?

A. 22 B. 2



235/280

C. D. 8


Answer: "ption C

Explanation:

4n 12 hours* the hands coincide or are in opposite direction 22 times.

4n 2 hours* the hands coincide or are in opposite direction times a da .


19. A +atch +hich gains uniforml is 2 minutes lo+ at noon on Gonda and is min. 8 sec fast at 2p.m. on the follo+ing Gonda . When +as it correct?

A. 2 p.m. on (uesda B. 2 p.m. on Wednesda

C. 3 p.m. on (hursda D. 1 p.m. on ;rida


Answer: "ption B

Explanation:

(ime from 12 p.m. on Gonda to 2 p.m. on the follo+ing Gonda $ da s 2 hours $ 1 0 hours.

(he +atch ga ins 2 min.

or3

min. in 1 0 hrs.! !

o+*3

min. are gained in 1 0 hrs.!

2 min. are gained in 1 0 %!

% 2hrs

$ !0 hrs.3

Watch is correct 2 da s 2 hrs. after 12 p.m. on Gonda i.e., it +ill e correct at 2 p.m. on

Wednesda .

NUMBER

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1. 4f one third of one fourth of a num er is 1!* then three tenth of that num er is,

A. 3! B. 36

C. ! D. !


Answer: "ption D

Explanation:


(hen*1

of 1

of x $ 1! x $ 1! % 12 $ 180.3

#o* re7uired num er $3

% 180 $ ! .10


2. (hree times the first of three consecuti-e odd integers is 3 more than t+ice the third. (he thirdinteger is,

A.9

B.11

C. 13 D. 1!


Answer: "ption D

Explanation:

&et the three integers e x * x 2 and x .

(hen* 3 x $ 2' x ) 3 x $ 11.

(hird integer $ x $ 1!.


3. (he difference et+een a t+o digit num er and the num er o tained interchanging the

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positions of its digits is 36. What is the difference et+een the t+o digits of that num er?

A. 3 B.


E. one of these


Answer: "ption B

Exp lanation:

&et the tenBs digit e x and unitBs digit e y .

(hen* '10 x y ) '10 y x ) $ 36

9' x y ) $ 36

x y $ .


. (he difference et+een a t+o digit num er and the num er o tained interchanging the digits is36. What is the difference et+een the sum and the difference of the digits of the num er if theratio et+een the digits of the num er is 1 , 2 ?

A. B. 8

C. 16 D. one of these


Answer: "ption B

Explanation:

#ince the num er is greater than the num er o tained on re-ersing the digits* so the tenBs digit isgreater than the unitBs digit.

&et t enBs and unitBs digits e 2 x and x respecti-el .

( he n* '10 % 2 x x ) '10 x 2 x ) $ 36



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9 x $ 36

x $ .

e7uired difference $ '2 x x ) '2 x x ) $ 2 x $ 8.


!. A t+o digit num er is such that the product of the digits is 8. When 18 is added to the num er*then the digits are re-ersed. (he num er is,

A. 18 B. 2

C. 2 D. 81


Answer: "ption B

Explanation:

&et the tenBs and unit digit e x and8

respecti-el . x

(hen* 10 x 8

18 $ 10 %8

x x x

10 x 2 8 18 x $ 80 x 2

9 x 2 18 x 2 $ 0

x 2 2 x 8 $ 0

' x )' x 2) $ 0

x $ 2.

6. (he sum of the digits of a t+o digit num er is 1! and the difference et+een the digits is 3. Whatis the t+o digit num er?

A. 69 B. 8




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E. one of these


Answer: "ption D

Explanation:


(hen* x y $ 1! and x y $ 3 or y x $ 3.

#ol-ing x y $ 1! and x y $ 3* +e get, x $ 9* y $ 6.

#ol-ing x y $ 1! and y x $ 3* +e get, x $ 6* y $ 9.

#o* the num er is either 96 or 69.

5ence* the num er cannot e determined.


. (he sum of the s7uares of three num ers is 138* +hile the sum of their products taken t+o at atime is 131. (heir sum is,

A. 20 B. 30



Answer: "ption A

Explanation:

&et the num ers e a * b and c .

(hen* a 2 b 2 c 2 $ 138 and ' ab bc ca ) $ 131.

'a c) 2 $ a 2 b 2 c 2 2' ab bc ca ) $ 138 2 % 131 $ 00.

' a b c ) $ 00 $ 20.




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8. A num er consists of t+o digits. 4f the digits interchange places and the ne+ num er is added tothe original num er* then the resulting num er +ill e di-isi le ,

A. 3 B. !

C. 9 D. 11


Answer: "ption D

Explanation:


(hen* num er $ 10 x y .

um er o tained interchanging the digits $ 10 y x .

' 10 x y ) '10 y x ) $ 11' x y )* +hich is di -isi le 11.


9. 4n a t+o digit* if it is kno+n that its unitBs digit e%ceeds its tenBs digit 2 and that the product ofthe gi-en num er and the sum of its digits is e7ual to 1 * then the num er is,

A. 2 B. 26

C. 2 D. 6


Answer: "ption A

Explanation:

&et the tenBs digit e x .

(hen* unitBs digit $ x 2.

um er $ 10 x ' x 2) $ 11 x 2.

# um of digits $ x ' x 2) $ 2 x 2.

'11 x 2)'2 x 2) $ 1



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22 x 2 26 x 1 0 $ 0

11 x 2 13 x 0 $ 0

' x 2)'11 x 3!) $ 0

x $ 2.

5ence* re7uired num er $ 11 x 2 $ 2 .


10. ;ind a positi-e num er +hich +hen increased 1 is e7ual to 60 times the reciprocal of thenum er.

A. 3 B. 10

C. 1 D. 20


Answer: "ption A

Explanation:


(hen* x 1 $60

x

x 2 1 x 60 $ 0

' x 20)' x 3) $ 0

x $ 3.

11. (he product of t+o num ers is 93 ! and the 7uotient* +hen the larger one is di-ided thesmaller* is 1!. (he sum of the num ers is,

A. 380 B. 39!

C. 00 D. 2!




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Answer: "ption C

Explanation:

&et the num ers e x and y .

(hen* xy $ 93 ! and x

$ 1!.y

xy $

93 !

' x / y ) 1!

y 2 $ 62!.

y $ 2!.

x $ 1! y $ '1! % 2!) $ 3 !.

#um of the num ers $ x y $ 3 ! 2! $ 00.


12. (he product of t+o num ers is 120 and the sum of their s7uares is 289. (he sum of the num eris,

A. 20 B. 23



Answer: "ption B

Explanation:


(hen* xy $ 120 and x 2

y 2

$ 289.

' x y ) 2 $ x 2 y 2 2 xy $ 289 '2 % 120) $ !29

x y $ !29 $ 23.




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13. A num er consists of 3 digits +hose sum is 10. (he middle digit is e7ual to the sum of the othert+o and the num er +ill e increased 99 if its digits are re-ersed. (he num er is,

A. 1 ! B. 2!3

C. 3 0 D. 3!2


Answer: "ption B

Explanation:

&et the middle digit e x .

(hen* 2 x $ 10 or x $ !. #o* the num er is either 2!3 or 3!2.

#ince the num er increases on re-ersing the digits* so the hundredBs digits is smaller than theunitBs digit.

5ence* re7uired num er $ 2!3.


1 . (he sum of t+o num er is 2! and their difference is 13. ;ind their product.

A. 10 B. 11

C. 31! D. 32!


Answer: "ption B

Explanation:


(hen* x y $ 2! and x y $ 13.

xy $ ' x y ) 2 ' x y ) 2

$ '2!) 2 '13) 2

$ '62! 169)



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$ !6

xy $ 11 .


1!. What is the sum of t+o consecuti-e e-en num ers* the difference of +hose s7uares is 8 ?

A. 3 B. 38

C. 2 D. 6


Answer: "ption C

Explanation:

&et the num ers e x and x 2.

( he n* ' x 2) 2 x 2 $ 8

x $ 8

x $ 80

x $ 20.

(he re7uired sum $ x ' x 2) $ 2 x 2 $ 2.

SIMPLIFICATION

1. A man has s. 80 in the denominations of one rupee notes* fi-e rupee notes and ten rupeenotes. (he num er of notes of each denomination is e7ual. What is the total num er of notes thathe has ?

A. ! B. 60

C. ! D. 90


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Ans wer: "ption D

Explanation:

&et num er of notes of each denomination e x .

(hen x ! x 10 x $ 80

16 x $ 80

x $ 30.

5ence* total num er of notes $ 3 x $ 90.


2. (here are t+o e%aminations rooms A and @. 4f 10 students are sent from A to @* then the num erof students in each room is the same. 4f 20 candidates are sent from @ to A* then the num er ofstudents in A is dou le the num er of students in @. (he num er of students in room A is,

A. 20 B. 80

C. 100 D. 200


Answer: "ption C

Explanation:

&et the num er of students in rooms A and @ e x and y respecti-el .

(hen* x 10 $ y 10 x y $ 20 .... 'i)

and x 20 $ 2' y 20) x 2 y $ 60 .... 'ii)

#ol-ing 'i) and 'ii) +e get, x $ 100 * y $ 80.

(he re7uired ans+er A $ 100.


3. (he price of 10 chairs is e7ual to that of ta les. (he price of 1! chairs and 2 ta les together iss. 000. (he total price of 12 chairs and 3 ta les is,

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A. s. 3!00 B. s. 3 !0

C. s. 38 0 D. s. 3900


Answer: "ption D

Explanation:

&et the cost of a chair and that of a ta le e s. x and s. y respecti-el .

(hen* 10 x $ y or y $!

x .2

1! x 2 y $ 000

1! x 2 %!

x $ 0002

20 x $ 000

x $ 200.

#o* y $!

% 200 $ !00.2

5ence* the cost of 12 chairs and 3 ta les $ 12 x 3 y

$ s. '2 00 1!00)

$ s. 3900.


. 4f a b $ 3 and a 2 b 2 $ 29* find the -alue of ab.

A. 10 B. 12

C. 1! D. 18


Answer: "ption A



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Explanation:

2ab $ ' a 2 b 2) ' a b ) 2

$ 29 9 $ 20

ab $ 10.


!. (he price of 2 sarees and shirts is s. 1600. With the same mone one can u 1 saree and 6shirts. 4f one +ants to u 12 shirts* ho+ much shall he ha-e to pa ?

A. s. 1200 B. s. 2 00

C. s. 800 D. Dannot e determined

E. one of these


Answer: "ption B

Explanation:

&et the price of a saree and a shirt e s. x and s. y respecti-el .

(hen* 2 x y $ 1600 .... 'i)

and x 6 y $ 1600 .... 'ii)

' 'd" "%&a 'on (') 2, :" " !" "/o: "%&a 'on.

=; x 2 = 800. --- (''')


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=; x 400 = 800

!"#"fo#" x = 400

# ol- ing 'i) and 'ii) +e get x $ 00* y $ 200.

Dost of 12 shirts $ s. '12 % 200) $ s. 2 00

6.A sum of s. 1360 has een di-ided among A* @ and D such that A gets of +hat @ gets and @

gets of +hat D gets. @Bs share is,

A. s. 120 B. s. 160

C. s. 2 0 D. s. 300


Answer: "ption C

Explanation:

&et DBs share $ s. x

(hen* @Bs share $ s. x

* ABs share $ s.2

% x

$ s. x

3 6

x +

x x $ 1360

6

1 x $ 1360

12

x $1360 % 12

$ s. 9601

5ence* @Bs share $ s.960

$ s. 2 0.


. "ne third of ahulBs sa-ings in ational #a-ings Dertificate is e7ual to one half of his sa-ings inu lic ro-ident ;und. 4f he has s. 1*!0*000 as total sa-ings* ho+ much has he sa-ed in u lic



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ro-ident ;und ?

A. s. 30*000 B. s. !0*000

C. s. 60*000 D. s. 90*000


Answer: "ption C

Explanation:

&et sa-ings in .#.D and . .;. e s. x and s. '1!0000 x ) respecti-el . (hen*

1 x

1'1!0000 x )

3 2

x +

x $ !000

3 2

! x $ !000

6

x $!000 % 6

$ 90000!

#a-ings in u lic ro-ident ;und $ s. '1!0000 90000) $ s. 60000


8. A fir es ! shots to @Bs 3 ut A kills onl once in 3 sh ots +hile @ kills once in 2 shots. When @ hasmissed 2 times* A has killed,

A. 30 irds B. 60 irds

C. 2 irds D. 90 irds


Answer: "ption A

Explanation:

&et the total num er of shots e x . (hen*



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#hots fired A $!

x 8

#hots fired @ $3

x

8

Jilling shots A $1

of !

x $!

x 3 8 2

#hots missed @ $1

of 3

x $3

x 2 8 16

3 x $ 2 or x $

2 % 16$ 1 .

16 3

@irds killed A $! x

$!

% 1 $ 30.2 2


9. =ight people are planning to share e7uall the cost of a rental car. 4f one person +ithdra+s fromthe arrangement and the others share e7uall the entire cost of the car* then the share of each ofthe remaining persons increased ,

A.1

B.1

8

C.

1

9 D.

8


Answer: "ption A

Explanation:

"riginal share of 1 person $1

8

e+ share of 1 person $ 1



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4ncrease $1 1

$1

8 !6

e7uired fraction $ ' 1/!6) $ 1 % 8 $ 1

'1/8) !6 1


10. (o fill a tank* 2! uckets of +ater is re7uired. 5o+ man uckets of +ater +ill e re7uired to fillthe same tank if the capacit of the ucket is reduced to t+o fifth of its present ?

A. 10 B. 3!

C. 62.! D. Dannot e determined

E. one of these


Answer: "ption C

Explanation:

&et the capacit of 1 ucket $ x .

(hen* the capacit of tank $ 2! x .

e+ capacit of ucket $2

x !

e7uired num er of u cke ts $2! x

'2 x /!)

$ 2! x

%!

2 x

$12!

2

$ 62.!

11. 4n a regular +eek* there are ! +orking da s and for each da * the +orking hours are 8. A man



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gets s. 2. 0 per hour for regular +ork and s. 3.20 per hours for o-ertime. 4f he earns s. 32 in +eeks* then ho+ man hours does he +ork for ?

A. 160 B. 1 !

C. 180 D. 19!


Answer: "ption B

Explanation:

#uppose the man +orks o-ertime for x hours.

o+* +orking hours in +eeks $ '! % 8 % ) $ 160.

160 % 2. 0 x % 3. 20 $ 32

3.20 x $ 32 38 $ 8

x $ 1!.

5ence* total hours of +ork $ '160 1!) $ 1 !.


12. ;ree note ooks +ere distri uted e7uall among children of a class. (he num er of note ooks eachchild got +as one eighth of the num er of children. 5ad the num er of children een half* eachchild +ould ha-e got 16 note ooks. (otal ho+ man note ooks +ere distri uted ?

A. 2!6 B. 32

C. !12 D. 6 0

E. one of these


Ans wer: "ption C

Exp lanation:

&et total num er of children e x .

(hen* x % 1 x $ x % 16 x $ 6 .



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8 2

um er of note ooks $1

x 2 $1

% 6 % 6 $ !12.

8 8View Answer Workspace Report Discuss in Forum

13. A man has some hens and c o+s. 4f the num er of heads e 8 and the num er of feet e7uals 1 0*then the num er of hens +ill e,

A. 22 B. 23

C. 2 D. 26


Ans wer: "ption D

Exp lanation:

&et the num er of hens e x and the num er of co+s e y .

(hen* x y $ 8 .... 'i)

and 2 x y $ 1 0 x 2 y $ 0 .... 'ii)

#ol-ing 'i) and 'ii) +e get, x $ 26* y $ 22.

(he re7uired ans+er $ 26.


1 . ' 69 1 ) 2 ' 69 1 ) 2

$ ?' 69 % 1 )

A. 2 B.

C. 29! D. 6 3


Answer: "ption B



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Explanation:

Ki-en e%p. $' a b ) 2 ' a b ) 2

ab

$ ab

ab

$ '+here a $ 69* b $ 1 .)


1!. a-id gets on the ele-ator at the 11 th floor of a uilding and rides up at the rate of ! floors perminute. At the same time* Al ert gets on an ele-ator at the !1st floor of the same uilding andrides do+n at the rate of 63 floors per minute. 4f the continue tra-elling at these rates* then at+hich floor +ill their paths cross ?

A. 19 B. 28

C. 30 D. 3


Answer: "ption C

Explanation:

#uppose their paths cross after x minutes.

(hen* 11 ! x $ !1 63 x 120 x $ 0

x 1

3

um er of floors co-ered a-id in '1/3) min. $1

% ! $ 19.3

# o* their paths cross at '11 19) i.e., 30 th floor.

RATIO & MIXTURE

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1.A and @ together ha-e s. 1210. 4f of ABs amount is e7ual to of @Bs amount* ho+ muchamount does @ ha-e?

A. s. 60 B. s. 8

C. s. !!0 D. s. 66


Answer: "ption B

Explanation:

A $2

@1! !

A $2

%1!

@!

A $3

@2

A$

3

@ 2

A , @ $ 3 , 2.

@Bs share $ s. 1210 %2

$ s. 8 .!


2. (+o num ers are respecti-el 20E and !0E more than a third num er. (he ratio of the t+onum ers is,

A. 2 , ! B. 3 , !

C. , ! D. 6 ,


Answer: "ption C

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Exp lanation:

&et the third num er e x .

(hen* first num er $ 120E of x $120 x

$6 x

100 !

#econd num er $ 1!0E of x $1!0 x

$3 x

100 2

atio of first t+o num ers $6 x

,3 x

$ 12 x , 1! x $ , !.! 2


3. A sum of mone is to e distri uted among A* @* D* in the proportion of ! , 2 , , 3. 4f D getss. 1000 more than * +hat is @Bs share?

A. s. !00 B. s. 1!00

C. s. 2000 D. one of these


Answer: "ption C

Explanation:

&et the shares of A* @* D and e s. ! x * s. 2 x * s. x and s. 3 x respecti-el .

(hen* x 3 x $ 1000

x $ 1000.

@Bs share $ s. 2 x $ s. '2 % 1000) $ s. 2000 .


. #eats for Gathematics* h sics and @iolog in a school are in the ratio ! , , 8. (here is aproposal to increase these seats 0E* !0E and !E respecti-el . What +ill e the ratio ofincreased seats?

A. 2 , 3 , B. 6 , , 8



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C. 6 , 8 , 9 D. one of these


Answer: "ption A

Explanation:

"riginall * let the num er of seats for Gathematics* h sics and @iolog e ! x * x and8 x respecti-el .

um er of increased seats are '1 0E of ! x )* '1!0E of x ) and '1 !E of 8 x ).

1 0% ! x *

1!0% x and

1 !% 8 x

100 100 100

x *21 x

and 1 x .2

(he re7uired ratio $ x ,21 x

, 1 x 2

1 x , 21 x , 28 x

2 , 3 , .


!. 4n a mi%ture 60 litres* the ratio of milk and +ater 2 , 1. 4f this ratio is to e 1 , 2* then the 7uanitof +ater to e further added is,

A. 20 litres B. 30 litres

C. 0 litres D. 60 litres


Answer: "ption D

Explanation:

Fuantit of milk $ 60 %2

litres $ 0 litres.3



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Fuantit of +ater in it $ '60 0) litres $ 20 litres.

e+ ratio $ 1 , 2

&et 7uantit of +ater to e added further e x litres.

(hen* milk , +ater $0

.20 x

o+*0

$1

20 x 2

20 x $ 80

x $ 60.

Fuantit of +ater to e added $ 60 litres.

6. (he ratio of the num er of o s and girls in a college is , 8. 4f the percentage increase in thenum er of o s and girls e 20E and 10E respecti-el * +hat +ill e the ne+ ratio?

A. 8 , 9 B. 1 , 18

C. 21 , 22 D. Dannot e determined


Answer: "ption C

Explanation:

"riginall * let the num er of o s and girls in the college e x and 8 x respecti-el .

( hei r increased num er is '120E of x ) and '110 E o f 8 x ).

120% x and

110% 8 x

10 0 100

math on train

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