A fraction becomes 1/2 if 2 is added to the numerator and 5 is added to the denominator, It also becomes 1/3 if 2 is subtracted from both the numerator and denominator. Then the fraction is

Correct option is A

Given:

A fraction becomes $$\frac{1}{2}$$​​ if 2 is added to the numerator and 5 is added to the denominator.

The fraction becomes $$\frac{1}{3}​$$​ if 2 is subtracted from both the numerator and denominator.

Solution:

Let the numerator of fraction be X, and denominator of fraction be Y

The fraction = $$\frac{X}Y$$​​

When 2 is added to its numerator and 5 added denominators

​$$\frac{x+2}{y+5}= \frac{1}{2}$$

​​2 (x+2)  =  y +5

2x− y =1........(1)

When 2 is subtracted from its numerator and denominator both

​$$\frac{x-2}{y-2}= \frac{1}{3}$$

​​3(x−2) = y−2 

3x−y = 4 .............(2)

Subtract Equation 1 from Equation 2 

(3x−y) − (2x−y) = 4−1

x = 3

Substitute x = 3 into Equation 1

2(3) −y =1

6-y = 1

y = 5 

the fraction is: $$\frac{x}{y}= \frac{3}{5}$$

Thus, correct option is (a)