Question

If we add 1 to the numerator and subtract 1 from the denominator a fraction reduces to 1. It becomes1/2 if we only add 1 to denominator what is the fraction?

Answer 1

Let the numerator be x

Let the denominator be y

Hence the fraction = x / y

Now,

If we add 1 to the numerator and subtract 1 from the denominator

$\frac{x + 1}{y - 1} = 1 \\ x + 1 = y - 1 \\ x - y = - 2$

Now,

if we only add 1 to denominator

$\frac{x}{y + 1} = \frac{1}{2} \\ 2x = y + 1 \\ 2x - y = 1$

x – y = – 2 – ( 1 )

2x – y = 1 – ( 2 )

( – ) ( + ) ( – )

_____________

– x = – 3

x = 3

Put x = 3 in ( 1 )

3 – y = – 2

– y = – 2– 3

y = 5

Ans : Fraction is :

$\frac{x}{y } = \frac{3}{5}$