Question

22. Find a fraction which becomes () when 1 is subtracted from the
numerator and 2 is added to the denominator, and the fraction becomes
(3) when 7 is subtracted from the numerator and 2 is subtracted from
the denominator.
​

Answer 1

Correct Question:-

Find a fraction which become 1/2 when 1 is subtracted from the numerator and 2 is added to the denominator and the fraction becomes 1/3 when 7 is subtracted from the numerator and 2 from denominator.

Answer:-

Let the fraction be x/y.

Given:

The fraction becomes 1/2 if 1 is subtracted from the numerator and 2 is added to denominator.

→ (x - 1) / (y + 2) = 1/2

On cross multiplication we get,

→ 2 (x - 1) = 1(y + 2)

→ 2x - 2 = y + 2

→ 2x - y = 2 + 2

→ 2x - y = 4 -- equation (1)

And,

The fraction becomes 1/3 if 7 is subtracted from numerator and 2 from denominator.

→ (x - 7) / (y - 2) = 1/3

→ 3 (x - 7) = y - 2

→ 3x - 21 = y - 2

→ 3x - y = - 2 + 21

→ 3x - y = 19 -- equation (2)

Subtract equation (1) from (2).

→ 3x - y - (2x - y) = 19 - 4

→ 3x - y - 2x + y = 15

→ x = 15

Substitute the value of x in equation (1)

→ 2 * 15 - y = 4

→ 30 - 4 = y

→ 26 = y

Therefore, the required fraction x/y is 15/26.