Question

A fraction become 5/8 if we substracts 2 from numerator and 3 from denominator .it becomes 10/9 if we add 3 to numerator and subtract 2 from denominator find the fraction

Answer 1

Answer:-

Let the fraction be x/y.

Given:

It becomes 5/8 if 2 is subtracted from numerator and 3 from denominator.

→ (x - 2)/(y - 3) = 5/8

On cross multiplication we get,

→ 8(x - 2) = 5(y - 3)

→ 8x - 16 = 5y - 15

→ 8x - 5y = - 15 + 16

→ 8x = 5y + 1

→ x = (5y + 1)/8 -- equation (1)

And,

It becomes 10/9 if we add 3 to numerator and subtract 2 from denominator.

→ (x + 3)/(y - 2) = 10/9

→ 9(x + 3) = 10(y - 2)

→ 9x + 27 = 10y - 20

→ 9x - 10y = - 20 - 27

Substitute x value from equation (1).

→ 9(5y + 1/8) - 10y = - 47

→ (45y + 9 - 80y)/8 = - 47

→ - 35y = (- 47 * 8) - 9

→ - 35y = - 376 - 9

→ - 35y = - 385

→ y = - 385/ - 35

→ y = 11

Putting the value of y in equation (1) we get,

→ x = [5(11) + 1]/8

→ x = 56/8

→ x = 7

Hence, the required fraction x/y is 7/11.