Question

If the numerator of a fraction is multiplied by 2 and the denominator is reduced by 5 the fraction becomes 6/5. And, if the denominator is doubled and the numerator is increased by 8, the fraction becomes 2/5. find the fraction.

Answer 1

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

If the numerator is multiplied by 2 and the denominator is reduced by 5, the fraction becomes. Thus, we have

If the denominator is doubled and the numerator is increased by 8, the fraction becomes. 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.

By using cross-multiplication, we have

Hence, the fraction is.