Answer:
The fraction is 
Option (B) is correct.
  and
  and 
Step-by-step explanation:
 Let n denotes numerator and d denotes denominator of the fraction.
Given : The ratio of the numerator to the denominator of a fraction is 2 to 3. 
That is  
 
Cross multiply , we get,
 
 
Or,  ........(1)
   ........(1)
 Also, given : . If both the numerator and the denominator are increased by 2, the fraction becomes 3/4
That is  
 
Cross multiply , We get,
 
 
 .........(2)
  .........(2)
 .......(3)
  .......(3)
Thus, from (1) and (2) , option (B) follows.
Solving equation (1) and (3) to get the original fraction using elimination method,
3n - 2d = 0    ............(1) 
and 3d - 4n = 2       .........(3)
Multiply equation (1) by 3 , we get ,
9n - 6d = 0  ..........(4)
Multiply equation (3) by 2 , we get ,
-8n + 6d = 4 ..........(5)
Adding (4) and  (5) , we get,
9n - 6d -8n + 6d = 4 + 0
⇒ n = 4 
Put n = 4 in (1), we get 
3n - 2d = 0 ⇒ 3(4) - 2d = 0 ⇒ 12 -2d = 0  ⇒  12 = 2d ⇒ d = 6
 so, the numerator is 4 and  the denominator is 6.
Thus, the fraction is 