Question

If 2 is added to the numerator and denominator, its become 9/10 and if 3 is subtracted from numerator and denominator, it becomes 4/5. Find the fraction. ​

Answer 1

Solution:-

Let the numerator of fraction be = x

Let the denominator of fraction be = y

if 2 is added to the numerator and denominator it

becomes = 9/10

=> x + 2 / y + 2 = 9/10

=> 10 ( x + 2 ) = 9 ( y + 2 )

=> 10x + 20 = 9y + 18

=> 10x - 9y = -2 .........(1)

if 3 is subtracted from numerator and denominator

it becomes 4/5.

=> x - 3 / y - 3 = 4/5

=> 5 ( x - 3 ) = 4 ( y - 3 )

=> 5x - 15 = 4y - 12

=> 5x - 4y = 3 .......(2)

From equation (1) and (2) we get,

multiply equation (1) by 4

multiply equation (2) by 9

we get,

=> 40x - 36y = -8

=> 45x - 36y = 27

we get,

=> - 5x = - 35

=> x = 7

put the value of x = 7 in equation (1)

we get,

=> 10(7) - 9y = -2

=> 70 - 9y = -2

=> - 9y = -72

=> y = 8

Therefore,

Fraction = 7/8