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NUMERICAL ABILITY

Directions (36-40): Study the following line graph carefully to answer the questions based on it.

The graph shows the number of infantry, horses and elephants in each army unit of six kings in a

certain year. Horses and elephants are being ridden by 1 and 4 soldiers respectively.

Q36. In a war, one unit of army of C and D each were made to stand on either side of midline of war

field. Both the units stand in rows such that each row contains same number of maximum possible

elements (i.e infantry, horses & elephants) of same category. Find the difference in total number of

rows in the two units? (The maximum possible elements in each row is different for both the units)

(a) 23

(b) 53

(c) 30

(d) 20

(e) None of these

Q37. In a war, 𝟖𝟑𝟏

𝟑% of total number of one army unit of king F

died. If the ratio of alive infantry, horses and elephants (with

soldiers) is 6 : 5 : 2, then find the number of infantry left alive.

(a) 95

(b) 105

(c) 86

(d) 90

(e) None of these


Q38. By what percent approximately the total number of soldiers in one army unit of king A is more or less than that of King E ?

(a) 25%

(b) 25.5%

(c) 23.5%

(d) 24%

(e) None of these

Q39. Kind D gave his 1 army unit to king A as dowry. King A sent that army unit along with his one army unit to king E. King E divided the infantry, horses and elephants of the two gifted units equally into his 5 army units. Find number of elephants in his new army unit. (Given that all unit has same number of three elements)

(a) 325

(b) 300

(c) 290

(d) 320

(e) 420

Q40. What is the ratio of average number of soldiers of 1 army unit of King F to the average number of infantry, horses and elephants of 1 army unit of king B ?

(a) 5 : 3

(b) 7 : 5

(c) 11 : 7

(d) 13 : 9

(e) None of these

Q41. The ratio of the first and second class train fares between two stations is 3 : 1 and that of the numbers of passengers travelling between the two stations by first and second classes is 1 : 50. If on a particular day, Rs. 1,325 are collected from passengers between the two stations then the amount collected from second class passengers is

(a) 1175 (b) 1250 (c) 1000 (d) 750 (e) None of these

Q42. A started a business with Rs. 52,000 and after 4 months B joined him with Rs. 39,000. At the end of the year, out of total profit B received total 20,000 including 25% of the profit as commission for managing the business. What amount did A receive ?

(a) 18,000 (b) 16,000 (c) 20,000 (d) 22,000 (e) None of these


Q43. A number is divided into two parts in such a way that 80% of Ist part is 3 more than 60% of 2nd part and 80% of 2nd part is 6 more than 90% of the 1st part then the number is :


Q44. In an examination, the average marks obtained by the students was found to be 60. After omission of computational errors, the average marks of 100 candidates had to be changed from 60 to 30 and the average with respect to all the examinees came down to 45 marks. The total number of candidates who took the exam, was:


Q45. A shopkeeper has 11 books of same cost price. He sells the first book at certain price, then he sells second book at a price which is Rs. 1 less than the selling price of first book and then he sells third book at a price which is Rs. 1 less than the selling price of second book. Following this pattern, he sold all 11 books. If he sells 6th book at its cost price, find the overall percentage profit or loss on selling all 11 books.

(a) 20% gain (b) 10% loss (c) 20% loss (d) 10% gain (e) No loss no gain

Directions (46-50): What will come in place of question mark (?) in the following number series ?

Q46. 30, 35, 65, 100, 165, 265, ?

(a) 270

(b) 520

(c) 430

(d) 395 (e) None of these

Q47. 3, 5, 7, ?, 13, 17

(a) 9

(b) 10

(c) 11

(d) 8

(e) None of these


Q48. 16, 17, 15, 18, 14, ?

(a) 10

(b) 17

(c) 18

(d) 20

(e) None of these

Q49. 3125, 256, ?, 4, 1

(a) 27

(b) 128

(c) 64

(d) 32

(e) None of these

Q50. 2, 3, 6, 18, 108, ?

(a) 126

(b) 1944

(c) 648

(d) 756

(e) None of these

Directions (51-55): In the following questions, two equations numbered I and II are given. You have

to solve both the equations and give answer

(a) if x>y

(b) if x≥y

(c) if x<y

(d) if x ≤y

(e) if x = y or relationship cannot be established

Q51. I. (6x2+17) −(3x2 +20) =0 II. (5y2−12) − (9y2−16) =0

Q52. I. (x+y) 2=3136 II. y+2513=2569

Q53. I. 17x=(13) 2+√196+(5) 2+4x II. 9y−345 = 4y−260

Q54. I. 679x2−168x2=3066 II. √144y3 −9y3 =1536

Q55. I. x2−16x+63=0 II. y2 −2y−35 = 0


Directions (56-60): Study the following table carefully to answer the questions that are based on it.

The table shows the dimensions of various types of iron blocks.

Blocks Length (cm) Breadth (cm) Height (cm) Radius (cm)

Cube 20 20 20 —

Cuboid 12 8 5 —

Sphere — — — 35

Cylinder 14 — — 8

Cone — — 28 21

Q56. Find the number of cones (of given dimension) that can be formed by melting 18 spheres of

given dimension.

(a) 252

(b) 265

(c) 250

(d) 270

(e) None of these

Q57. Find the cost of painting 630 conical blocks of given dimension provided that only the curved

surface area is to be painted at Rs. 5 per m2. (approx.)

(a) Rs. 777

(b) Rs. 727

(c) Rs. 780

(d) Rs. 725

(e) Rs. 790

Q58. Find the total number of cubical blocks of given dimension required to raise the water level to

the brim of a cylindrical container having dimensions 10 times than that of the given cylinder.

Initially container is half filled.

(a) 176

(b) 80

(c) 220

(d) 128

(e) None of these

Q59. Find the ratio of total surface area of cylinder, cone and sphere.

(a) 88 : 294 : 1225

(b) 575 : 352 : 89

(c) 18 : 119 : 54

(d) 2 : 8 : 13

(e) 5 : 17: 7


Q60. By what percent the total surface area of cuboid is more or less than the lateral surface area

of cube ?

(a) 70.5%

(b) 65%

(c) 75.5%

(d) 80%

(e) None of these

Q61. The compound interest on a certain sum of money at a certain rate per annum for 2 years is

Rs. 2,050, and the simple interest on the same amount of money at the same rate for 3 years is Rs.

3000. Then the sum of money is:

(a) 18,000

(b) 21,000

(c) 20,000

(d) 25,000

(e) None of these

Q62. A businessmen bought an article and sold it at a loss of 5%. If he had bought it for 10% less

and sold it for Rs. 33 more, he would have had a profit of 30%. The cost price of the article is :

(a) Rs. 330

(b) Rs. 155

(c) Rs. 150

(d) Rs. 300

(e) None of these

Q63. A can complete a piece of work in 10 days, B in 15 days and C in 20 days, A and C worked

together for two days and then A was replaced by B. In how many days, altogether, work was

completed ?

(a) 12 days

(b) 10 days

(c) 6 days

(d) 8 days

(e) None of these

Q64. Ravi and Ajay start simultaneously from a place A towards B, 60 km apart. Ravi’s speed is 4

km/hr less than that of Ajay. After reaching B, Ajay turns back and meet Ravi at a place 12 km away

from B, Ravi’s speed is :

(a) 12 km/hr

(b) 10 km/hr

(c) 8 km/hr

(d) 6 km/hr

(e) None of these


Q65. There are 42 men and 16 women in a party. Each man shakes his hand only with all the men and each woman shakes her hand only with all the women. Find the maximum no. of handshakes that have taken place at the party.


Directions (66-70): What approximate value should come in place of question mark (?) in the following questions ?

Note: You are not expected to calculate the exact value.

Q66. 126.99% of 1539.98 + 5.5% of 149.99 + 103.98% of 7 = ? (a) 1960 (b) 1970 (c) 1980 (d) 1950 (e) 1955

Q67. √𝟑𝟔𝟎. 𝟗𝟖 × 𝟏𝟖. 𝟗𝟗 + 𝟏𝟎𝟖𝟐. 𝟗𝟖 ÷ 𝟓𝟕. 𝟎𝟕 =? (a) 372 (b) 380 (c) 386 (d) 389 (e) 390

Q68. 94.95× 13.09 + √𝟑𝟓. 𝟗𝟖 × 𝟏𝟒. 𝟗𝟗 = 𝟓𝟑 × √?

(a) 25 (b) 144 (c) 225 (d) 625 (e) 900

Q69. (333% of 856) ÷ 49.95 = ?

(a) 43 (b) 41 (c) 47 (d) 39 (e) 57

Q70. √𝟏𝟖𝟓𝟎 × 𝟒𝟒. 𝟗𝟖% 𝒐𝒇 𝟏𝟔𝟖𝟎. 𝟑𝟐𝟏 =? × 𝟑𝟎𝟎. 𝟗𝟖𝟔

(a) 108 (b) 164 (c) 92 (d) 204 (e) 146


Solutions

S36. Ans.(c)

Sol. Number of elements in each row = H.C.F. of three categories

∴ Total no. of elements in unit of king C = H.C.F. of 480, 400 and 180 = 20

So, total number of rows =480

20+

400

20+

180

20= 53

Similarly, total number of rows in unit of king D =500

50+

450

50+

200

50= 23

∴ Required difference = 53 – 23 = 30

S37. Ans.(d)

Sol. Number of soldiers left = 162

3% of (650 + 420 + 160 × 4) = 285

Then, according to question,

6𝑥 + 5𝑥 + (2 × 4)𝑥 = 285 ⇒ 𝑥 =285

19= 15

∴ Required number of soldiers = 15 × 6 = 90

S38. Ans.(b)

Sol. Total soldiers of A = 540 + 350 + 150 × 4 = 1490

Total soldiers of E = 750 + 250 + 250 × 4 = 2000

∴ Required percentage =510

2000× 100 = 25.5%

S39. Ans.(d)

Sol. Required number of elephants = 250 +200+150

5 = 320

S40. Ans. (e)

Sol. Required ratio

=

1

3× (650 + 420 + 160 × 4)

1

3× (620 + 370 + 120)

=1710

1110=

57

37

S41. Ans.(b)

Sol.

⇒ 53𝑥 = 1325

∴ 𝑥 =1325

53= 25

∴ Amount collected from IInd class = 50𝑥

⇒ 25 × 50 = Rs. 1250


S42. Ans.(c)

Sol. Investment ratio of A and B = 52000 × 12 : 39000 × 8 = 2 : 1

Let profit be 100 unit

Now 25% profit given to B as commission

So, (100 – 25) = 75 unit divided between A & B in ratio 2 : 1

∴ B get total profit = 25 + 75 ×1

3= 50 unit

⇒ 50 unit = 20,000

⇒ 1 unit = 400

∴ A’s share = 75 × 2

3 = 50 unit

⇒ 50 × 400 = 20,000

S43. Ans.(a)

Sol. Let the first and second part of a number is 𝑎 and 𝑏 respectively.

According to the question,

Case: (i) 80

100𝑎 −

60

100𝑏 = 3

⇒ 8𝑎 − 6𝑏 = 30 … (𝑖)

Case: (ii) 80

100𝑏 −

90

100𝑎 = 6

8𝑏 − 9𝑎 = 60 … (𝑖𝑖)

From eqn. (i) & (ii)

𝑎 = 60, 𝑏 = 75

Hence required number = (𝑎 + 𝑏) = (60 + 75) = 135

S44. Ans.(a)

Sol. According to the question,

Let the number of students = 𝑥

∴ 60𝑥 − 3000 = 45𝑥

∴ 𝑥 = 200

S45. Ans.(e)

Sol. Let S.P. of 1st book = 𝑛

Then

S.P. of total 11 books = 𝑛 + 𝑛 − 1 + … + 𝑛 − 5 + … + 𝑛 − 10 = 11𝑛 − 55

⇒ S.P. of 6th books = C.P. of 1 book = 𝑛 − 5

C.P. of all book = (𝑛 − 5) × 11

= 11𝑛 − 55

⇒ S.P. = C.P.

∴ No gain no loss


S46. Ans.(c)

Sol. 30 + 35 = 65

65 + 35 = 100

100 + 65 = 165

165 + 100 = 265

265 + 165 = 430

S47. Ans.(b)

Sol.

S48. Ans.(e)

Sol.

S49. Ans.(a)

Sol.

3125↓

(5)5

256↓

(4)4

27

↓(3)3

4↓

(2)2

1↓

(1)1

S50. Ans.(b)

Sol.

S51. Ans.(e)

Sol. 3𝑥2 = 3

𝑥2 = 1, 𝑥 = 1, −1

4𝑦2 = 4, 𝑦 = 1, −1

So no relation can be established.

S52. Ans.(c)

Sol. 𝑦 = 56

𝑥 + 𝑦 = 56, 𝑥 = 0

𝑥 < 𝑦


S53. Ans.(c)

Sol. 13𝑥 = 169 + 14 + 25 = 208

𝑥 = 16

5𝑦 = 85, 𝑦 = 17

𝑥 < 𝑦

S54. Ans.(c)

Sol. 𝑥 = √6, −√6

𝑦 = 8

𝑥 < 𝑦

S55. Ans.(b)

Sol. 𝑥2 − 9𝑥 − 7𝑥 + 63 = 0

𝑥(𝑥 − 9) − 7(𝑥 − 9) = 0

𝑥 = 7, 9

𝑦2 − 7𝑦 + 5𝑦 − 35 = 0

𝑦(𝑦 − 7) + 5(𝑦 − 7) = 0

𝑦 = −5, 7

𝑥 ≥ 𝑦

S56. Ans.(c)

Sol. Let 𝑛 number of cones are formed.

So,

Volume of 𝑛 cones = Volume of 18 spheres

⇒ 𝑛 ×1

3× 𝜋 × 212 × 28 = 18 ×

4

3× 𝜋 × 353

⇒ 𝑛 = 250

S57. Ans.(b)

Sol. Slant height of cone = √212 + 282 = 35 cm

∴ Required cost of painting = 630 ×22

7× 21 × 35 ×

5

1002

≈ 727

S58. Ans.(a)

Sol. Volume of container =22

7× 802 × 140

= 2816000 cm3

∴ Volume of required number of cubical blocks should be equal to half the volume of container

So, 𝑥 × 203 =2816000

2

⇒ 𝑥 = 176


S59. Ans.(a)

Sol. Required ratio = 2π × 8(8 +14) : π × 21 (21 + 35) : 4π × 352

= 352 : 1176 : 4900

= 88 : 294 : 1225

S60. Ans.(c)

Sol. T.S.A. of cuboid = 2(12 × 8 + 8 × 5 + 5 × 12)

= 392 cm2

L.S.A. of cube = 4 × 202 = 1600 cm2

∴ Required percentage =1208

1600× 100 = 75.5%

S61. Ans.(c)

Sol. SI of 3 years = Rs. 3000

SI for 2 years = Rs.3000

3× 2 = Rs. 2000

SI for 2 years = Rs.2000

CI for 2 years = Rs. 2050

difference = (2050 – 2000) = Rs. 50

Required rate% =50

1000× 100 = 5%

According to the question,

5% of sum = 1000

sum =1000

5× 100 = Rs. 20,000

S62. Ans.(c)

Sol. Let CP of the article = 100𝑥

According to question,

SP = 95𝑥

Again,

New CP = 90𝑥

Then,

New SP = 90𝑥 ×130

100= 117𝑥

Difference between new SP and actual SP

⇒ 117𝑥 − 95𝑥 = 33

⇒ 22x = 33

∴ 𝑥 =3

2

∴ CP of article = 100𝑥 = 100 ×3

2 = 150


S63. Ans.(d)

Sol.

A and C work for two days = (6 + 3) × 2 = 18 units

Work left = (60 – 18) = 42 units

Now A is replaced by B

(B + C) one day work = 4 + 3

(B + C) complete remaining work in — total work

Eff.=

42

7= 6 days.

Total days = 6 + 2 = 8 days

S64. Ans.(c)

Sol. Let the speed of Ravi = 𝑥 km/hr

Then; Ajay’s speed will be (𝑥 + 4) km/hr.

Total distance, covered by Ajay = 60 + 12 = 72 km

Total distance, covered by Ravi = 60 – 12 = 48 km

According to question,

⇒72

(𝑥+4)=

48

𝑥

⇒ 72𝑥 = 48𝑥 + 192 ⇒ 24𝑥 = 192 ⇒ 𝑥 = 8 km hr⁄ . ∴ Ravi’s speed = 8 km/hr.

S65. Ans.(b)

Sol. Total no. of handshakes among the group of 42 men

⇒ 𝐶2 42 =

42!

2!(42−2)!=

42!

2!40!

=42×41×40!

2×1×40!

= 21 × 41 = 861 Total no. of handshakes among the group of 16 women

⇒ C2 16 =

16!

2!(16−2)!=

16!

2!14! =

16×15×14!

2×1×14!

= 8 × 15 = 120 ∴ Maximum no. of handshakes = 861 + 120 = 981.

S66. Ans.(b)

Sol. ? = (127

100× 1540) + (

5.5

100× 150) + (

104

100× 7)

= 1955.8 + 8.25 + 7.28

= 1971.33 ≈ 1970


S67. Ans.(b)

Sol. ? = √361 × 19 + 1083 ÷ 57 ≈ 380

S68. Ans.(d)

Sol. (95 × 13) + (6 × 15) = 53 × √?

⇒ 1235 + 90 = 1325 = 53 × √?

⇒ 53 × 25 = 53 × √?

⇒ ? = 625

S69. Ans.(e)

Sol. (333% of 856) ÷ 49.95

= 2850.48 ÷ 49.95

≈ 2850 ÷ 50 = 57

S70. Ans.(a)

Sol. ≈43×45×1680

100×301 = 108

1 adda247 | no. 1 app for banking & ssc preparation website · q45. a shopkeeper has 11 books...

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