26.1. Find the fraction which becomes when thedenominator is increased

1.	26.1. Find the fraction which becomes when thedenominator is increased by 4 and is equal towhen numerator is diminished by 5
Answer» Let the fraction be x/y. The fraction becomes 1/2 when the denominator is increased by 4 ⇒ x / (y + 4) = 1/2⇒ 2x = y + 4⇒ 2x - y = 4 -------------------------- (1) The fraction is equal to 1/8 when the numerator is diminished by 5 ⇒ (x - 5) / (y) = 1/8⇒ 8x - 40 = y⇒ 8x - y = 40 -------------------------- (2) Solving equations (1) and (2), we get x = 6 and y = 8. Therefore, the required fraction is 6/8.

26.1. Find the fraction which becomes when thedenominator is increased by 4 and is equal towhen numerator is diminished by 5

Answer»

Let the fraction be x/y.

The fraction becomes 1/2 when the denominator is increased by 4

⇒ x / (y + 4) = 1/2⇒ 2x = y + 4⇒ 2x - y = 4 -------------------------- (1)

The fraction is equal to 1/8 when the numerator is diminished by 5

⇒ (x - 5) / (y) = 1/8⇒ 8x - 40 = y⇒ 8x - y = 40 -------------------------- (2)

Solving equations (1) and (2), we get x = 6 and y = 8.

Therefore, the required fraction is 6/8.