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Question

If $1$ is added to the denominator of a fraction, the fraction becomes $\frac{1}{2}$ . If $1$ is added to the numerator of the fraction. the fraction becomes $1$ . Then the fraction is

A

$\frac{3}{4}$

B

$\frac{4}{5}$

C

$\frac{1}{2}$

D

$\frac{2}{3}$

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Solution

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Correct option is D)

Let the numerator be n and the denominator be d. Then
$\frac{n}{d + 2} = \frac{1}{2}$ ........... (1)
or $2 n = d + 1$
$\frac{n + 1}{d} = 1$
or $n + 1 = d$ ............(2)
Substituting for d in equation (1), we get
$2 n = n + 1 + 1$
or $2 n - n = 2$
or $n = 2$
$∴ d = n + 1 = 2 + 1 = 3$
Hence, $\frac{n}{d} = \frac{2}{3}$

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