Question

The numerator of a fraction is 4 less than the denominator. If the numerator is decreased by 2 and denominator is increased by 1, then the denominator is eight times the numerator. Find the fraction.

Answer 1

Let the numerator and denominator of the fraction be x and y respectively. Then the fraction is

The numerator of the fraction is 4 less the denominator. Thus, we have

If the numerator is decreased by 2 and denominator is increased by 1, then the denominator is 8 times the numerator. Thus, we have

So, we have two equations

Here x and y are unknowns. We have to solve the above equations for x and y.

Subtracting the second equation from the first equation, we get

Substituting the value of x in the first equation, we have

Hence, the fraction is.