Question

If 1 is added to the numerator of a fraction, it becomes 1/5; if 1 is taken away from the denominator, it becomes 1/7. Find the fraction.

Answer 1

Let the numerator of fraction be x and denominator be y

By the first condition given in your question we get equation

x + 1/y = 1/5

( x + 1 ) 5 = y

5x + 5 = y

5x - y = - 5. ... ( l )

By the second condition given in your question we get equation

x / y - 1 = 1/7

7x = y - 1

7x - y = - 1

subtracting equation ( l ) from equation ( ll )

2x = 4

x = 2

putting x = 2 in equation ( l ) we get

5 ( 2 ) - y = -5

10 - y = - 5

y = 5

fraction = 2/5