7/28/2019 2.4 Algebra

1/5

Subject Topic Assignment Number Mathematics Algebra NTSE-M-AL-2.4-HA

1

Q1 Solve:

(i) 2738 x (ii) 813 xC1 (i) 2738 x

8 27 3

8 24

248

3

x

x

x

x

(ii) 813 x

3 3 8

3 8 3

3 11

113

x

x

x

x

Q2Solve 4

57

y y

C2457 y y

7 5( 4)

7 5 20

7 5 20

2 20

2010

210

y y

y y

y y

y

y

y

Q3Solve 32

21

342

5 z z

C3 3221

342

5 z z

7/28/2019 2.4 Algebra

2/5

Subject Topic Assignment Number Mathematics Algebra NTSE-M-AL-2.4-HA

2

15 2 8 1 2 33 2

2( 2 23) 3(2 3)

4 46 6 9

4 6 9 46

10 37

3710

z z

z z

z z

z z

z

z

Q4Solve

23

344

53 y y

y

C4 2

334

453 y

y y

3 5 16 6 34 2

3 15 16 2(9 )

13 15 18 2

13 2 18 15

11 33

33311

y y y

y y y

y y

y y

y

y

Q5Solve

54

41792

y y

C5

54

41792

y y

5(2 9 ) 4(17 4 )

10 45 68 16

45 16 68 1029 58

582

29

(By cross multiplication) y y y y

y y y

y

7/28/2019 2.4 Algebra

3/5

Subject Topic Assignment Number Mathematics Algebra NTSE-M-AL-2.4-HA

3

Q6

32

of a number is 20 less than the original number. Find the number.

C6 Let the original number be x .

Given:

2( ) 20

32 3( 20)

2 3 60

2 3 60

6060

x x

x x

x x

x x

x x

the original number is 60

Q7 Two numbers are such that the ratio between them is 5:3 . If each is increased

by 10, the ratio between the new numbers so formed is 7:5 . Find the original

numbers.

C7 Let the original numbers be 3 & 5 x x

Given:3 10 55 10 7 x x

7(3 10) 5(5 10)

21 70 25 50

21 25 50 70

4 20 5

x x

x x

x x

x x

the original numbers are 15 and 25

Q8 Divide 150 into three parts such that the second number is five-sixths the first

and the third number is four-fifth the second.

C8Given: second number =

56

(first number) ___(1)

7/28/2019 2.4 Algebra

4/5

Subject Topic Assignment Number Mathematics Algebra NTSE-M-AL-2.4-HA

4

third number =45

(second number)

=4 55 6

(first number)

[sub. From (1)]

=23

(first number)

150 = first number +56

(first number) +23

(first number)

Let the first number be x .

5 2150

6 36 5 4

6150 6 15

60

x x x

x x x

x

x

The first part = 60

Second number =5

(60) 506 and

Third number =2

(60) 403

Q9 Find three consecutive even numbers whose sum is 234.

C9 Let the even numbers be , 2 4 x x and x

Then

2 4 234

3 6 2343 234 6

228

22876

3

x x x

x x

x

the three consecutive even numbers are 76, 78, 80

7/28/2019 2.4 Algebra

5/5

Subject Topic Assignment Number Mathematics Algebra NTSE-M-AL-2.4-HA

5

Q10 Rakhis mother is four times as old as Rakhi. After 5 years, her mother will be

three times as old as she will be then. Find their present ages.C10 Let Rakhis present age be x years.

Her mothers present age be 4 x years.

After 5 years,

Rakhis age will be 5 x years.

Her mothers age will be 4 5 x years.

According to the given condition, we have

4 5 3 5 x x

4 5 3 15 x x

4 3 15 5 x x

10 x

Rakhis present age = 10 years. Her mothers age = 40 years