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RD Chapter 3 Pair of Linear Equations in Two Variables Ex 3.8 Solutions

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)

Answer - 1 : -

Let numerator of a fraction = x
and denominator = y
Then fraction = 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 = x/y

Question - 2 : - A fraction becomes 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 5/6. Find the fraction. (C.B.S.E. 1990)

Answer - 2 : -

Let the numerator of a fraction = x
and denominator = y
Fraction = x/y = 7/9

Question - 3 : - A fraction becomes 1/3 if 1 is subtracted from both its numerator and denominator. If 1 is added to both the numerator and denominator, it becomes 1/2. Find the fraction. (C.B.S.E. 1993C)

Answer - 3 : -

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 1/2 if we only add 1 to the denominator. What is the fraction.

Answer - 4 : -

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 1/2. Find the fraction. (C.B.S.E. 2006C)

Answer - 5 : -

Let the numerator of a fraction = x
and denominator = y

Fraction= x/y = 5/7

Question - 6 : - When 3 is added to the denominator and 2 is subtracted from the numerator a fraction becomes 1/4. And, when 6 is added to numerator and the denominator is multiplied by 3, it becomes 2/3. Find the fraction.

Answer - 6 : -

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 1/3. Find the fraction. (C.B.S.E. 1997C)

Answer - 7 : -

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 1/2 and if 1 is subtracted from the denominator, it 1 reduces to 1/3. Find the fraction. (C.B.S.E. 1997C)

Answer - 8 : -

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)

Answer - 9 : -

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 6/5. And, if the denominator is doubled and the numerator is increased by 8, the fraction becomes 2/5. Find the fraction.

Answer - 10 : -

Let the numerator of fraction = x
and denominator = y

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