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The sum of numerator and the denominator of a fraction is 12. If the denominator is increased by 3, the fraction becomes $1 / 2$ . Find the fraction.

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\frac{5}{7}

\frac{5}{6}

\frac{4}{7}

\frac{7}{7}

answer is A.

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Detailed Solution

Given,
Sum of numerator and denominator of a fraction = 12
Let the required fraction be

\frac{x}{y}

. then,

x + y = 12

....(1)
So,

\frac{x}{y + 3} = \frac{1}{2}

2 x - y = 3

...(2)
Add equation (1) and (2),

x + y + (2 x - y) = 12 + 3

3 x = 15

x = 5

Put the value of

x

in equation (1),

x + y = 12

5 + y = 12

y = 12 - 5

y = 7

So the needed fraction

\frac{x}{y} = \frac{5}{7}

Option 1 is correct.

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