CBSE Class 10 Answered

Let the fraction be  ( x / y )

If 2 is added to numerator and denominator , then the fraction becomes ( 9 / 11 )

i.e.  11 ( x +2 ) = 9 ( y + 2 )

11x - 9y = -4 ...................(1)

If 3 is added to numerator and denominator , then the fraction becomes ( 5 / 6 )

i.e.  6x+18 = 5y + 15

6x-5y = -3 .........................(2)

From above expression, we get

y = (3/5) ( 2 x+ 1 ) ................(3)

Substituting y from eqn.(3) , let us re write eqn.(1) as

11 x - 9 ( 3/5) ( 2x+1 ) = -4

[ 11 - (54/5) ] x = - 4 + (27/5)

(1/5) x = (7/5)

x = 7

by substituting x = 7 in eqn.(3) , we get y = 9

Fraction is  ( x / y ) = 7/9