Question

The numerator of the given fraction is 4 less than the denominator. If 5 is added to both numerator and denominator, the resulting fraction is equivalent to 5/7 . What is the original fraction?

Answer 1

5/9

Explanation:

Let the denominator be x and numerator be y.

Given, numerator is 4 less than denominator

=> y = x - 4 ...(1)

When 5 is added to both:

Numerator = y + 5 , and, denominator = x + 5

Now their ratio is 5/7.

=> (y + 5)/(x + 5) = 5/7

=> 7(y + 5) = 5(x + 5)

=> 7y + 35 = 5x + 25

=> 7y - 5x = 25 - 35

=> 7(x - 4) - 5x = -10 {y=x-4}

=> 7x - 28 - 5x = -10

=> 2x = 18

=> x = 9

Thus,

Fraction is y/x = (x-4)/x = (9-4)/9 = 5/9