## Pair of Linear Equations in Two Variables Class 10 Solutions Exercise 3.8

### RD Sharma Class 10 Solutions Pair Of Linear Equations In Two Variables Exercise 3.8

Question 1.

The numerator of a fraction is 4 less than the denominator. If the numerator is decreased by 2 and denominator is increased by 1, then the denominator is eight times the numerator. Find the fraction. (C.B.S.E. 1990)

Solution:

Let numerator of a fraction = x

and denominator = y

Then fraction = \(\frac { x}{ y}\)

According to the conditions,

y – x = 4 ….(i)

and 8 (x – 2) = y + 1

⇒ 8x – 16 – y + 1

⇒ 8x – y = 1 + 16

⇒ 8x – y= 17 ….(ii)

Adding (i) and (ii)

7x = 21 ⇒ x = 3

y – 3 = 4

⇒ y = 4 + 3 = 7

Hence fraction = \(\frac { x}{ y}\)

Question 2.

A fraction becomes \(\frac { 9 }{ 11 }\) if 2 is added to both numerator and the denominator. If 3 is added to both the numerator and the denominator, it becomes \(\frac { 5 }{ 6 }\). Find the fraction. (C.B.S.E. 1990)

Solution:

Let the numerator of a fraction = x

and denominator = y

Fraction = \(\frac { x}{ y}\) = \(\frac { 7 }{ 9 }\)

Question 3.

A fraction becomes \(\frac { 1 }{ 3 }\) if 1 is subtracted from both its numerator and denominator. If 1 is added to both the numerator and denominator, it becomes \(\frac { 1 }{ 2 }\). Find the fraction. (C.B.S.E. 1993C)

Solution:

Let the numerator of a fraction = x

and denominator = y

Question 4.

If we add 1 to the numerator and subtract 1 from the denominator, a fraction becomes 1. It also becomes \(\frac { 1 }{ 2 }\) if we only add 1 to the denominator. What is the fraction.

Solution:

Let numerator of a fraction = x

and denominator = y

Question 5.

The sum of the numerator and denominator of a fraction is 12. If the denominator is increased by 3, the fraction becomes \(\frac { 1 }{ 2 }\). Find the fraction. (C.B.S.E. 2006C)

Solution:

Let the numerator of a fraction = x

and denominator = y

Fraction = \(\frac { x}{ y}\) = \(\frac { 5 }{ 7 }\)

Question 6.

When 3 is added to the denominator and 2 is subtracted from the numerator a fraction becomes \(\frac { 1 }{ 4 }\). And, when 6 is added to numerator and the denominator is multiplied by 3, it becomes \(\frac { 2 }{ 3 }\). Find the fraction.

Solution:

Let numerator of a fraction = x

and denominator = y

Question 7.

The sum of a numerator and denominator of a fraction is 18. If the denominator is increased by 2, the fraction reduces to \(\frac { 1 }{ 3 }\). Find the fraction. (C.B.S.E. 1997C)

Solution:

Let the numerator of a fractrion = x

and denominator = y

Question 8.

If 2 is added to the numerator of a fraction, it reduces to \(\frac { 1 }{ 2 }\) and if 1 is subtracted from the denominator, it 1 reduces to \(\frac { 1 }{ 3 }\). Find the fraction. (C.B.S.E. 1997C)

Solution:

Let the numerator of a fraction = x

and denominator = y

Question 9.

The sum of the numerator and denominator of a fraction is 4 more than twice the numerator. If the numerator and denominator are increased by 3, they are in the ratio 2 : 3. Determine the fraction (C.B.S.E. 2001C)

Solution:

Let the numerator of a fraction = x

and denominator = y

Question 10.

If the numerator of a fraction is multiplied by 2 and the denominator is reduced by 5 the fraction becomes \(\frac { 6 }{ 5 }\). And, if the denominator is doubled and the numerator is increased by 8, the fraction becomes \(\frac { 2 }{ 5 }\). Find the fraction.

Solution:

Let the numerator of fraction = x

and denominator = y

Question 11.

The sum of the numerator and denominator of a fraction is 3 less than twice the denominator. If the numerator and denominator are decreased by 1, the numerator becomes half the denominator. Determine the fraction. (C.B.S.E. 2001C)

Solution:

Let the numerator of a fraction = x

and denominator = y

Then fraction = \(\frac { x }{ y }\)

According to the conditions given,

x + y = 2y – 3

⇒ x + y – 2y = -3

### Pair of Linear Equations in Two Variables Class 10 Solutions Exercise 3.8

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#### RD Sharma Class 10 Solutions

- Pair Of Linear Equations In Two Variables Ex 3.1
- Pair Of Linear Equations In Two Variables Ex 3.2
- Pair Of Linear Equations In Two Variables Ex 3.3
- Pair Of Linear Equations In Two Variables Ex 3.4
- Pair Of Linear Equations In Two Variables Ex 3.5
- Pair Of Linear Equations In Two Variables Ex 3.6
- Pair Of Linear Equations In Two Variables Ex 3.7
- Pair Of Linear Equations In Two Variables Ex 3.8
- Pair Of Linear Equations In Two Variables Ex 3.9
- Pair Of Linear Equations In Two Variables Ex 3.10
- Pair Of Linear Equations In Two Variables Ex 3.11