When the numerator and the denominator of a fraction are increased by 1 and 2 respectively, the fraction becomes `(2)/(3)`, and when the numerator and the denominator of the same fraction are increased by 2 and 3 respectively, the fraction becomes `(5)/(7)`.What is the original fraction ?

Options

A. `(5)/(6)`
B. `(3)/(4)`
C. `(3)/(5)`
D. `(6)/(7)`

Answer

B

Explanation

`(x+1)/(y+2)=(2)/(3)rArr 3x -2y=1`
`(x+2)/(y+3)=(5)/(7)rArr 7x-5y=1`
or, `3x-2y=7x-5yrArr 3y=4xrArr (x)/(y)=(3)/(4)`