Question

The denominator of a rational number is greater than the numerator by 6. if the numerator is decreased by 2 and the denominator increased by 4,the new rational number becomes 1/5 . find the original rational number.

Answer 1

Let numerator= x
Let denomenator= y

ATQ      1st case
              y= x+6. . . .(1)
2nd case
   x-2/y+4= 1/5
  5(x-2)= y+4
  5x-10= x+6+4                  (∴y= x+6)
  5x-x= 10+10
  4x= 20
  x= 20/4= 5. . . .(2)
Putting (2) in (1)
y= 5+6= 11
                      ∵Rational number= 5/11