if the numinator and denominatar of a fracrion is increased by 2 the fraction become 5/7 and if its denominator is decreased by 1 the fraction becomes 3/4 . find the fraction ?
Ans:
Let the fraction be x/y
The first statement tells us that 
i.e 
Simplifying
 ----> (1)
The second statement tells us that 
i.e. 
Simplifying
 -----> (2)
The set of 2 simultaneous equations (1) and (2) can be solved using the solver available in this site, as shown below.


 
Solved by pluggable solver: SOLVE linear system by SUBSTITUTION
Solve:
  We'll use substitution. After moving -5*y to the right, we get:
  , or . Substitute that
  into another equation:
   and simplify: So, we know that y=5. Since , x=3.
  
  Answer: .
  


We get the solution as x = 3, y = 5
Hence the fraction is 
Check: Adding 2 to numerator and denominator, we get 5/7
Subtracting 1 from denominator, the fraction becomes 3/4. Correct!

Hope this helps :)