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Question : 5 of 39

Marks: +1, -0

The denominator of a fraction exceeds the numerator by 7 and if the 2 is added to the denominator 4 then the fraction becomes

\frac{4}{7}

. Find the fraction.

$\frac{12}{19}$
$\frac{7}{14}$
$\frac{9}{16}$
$\frac{11}{18}$

Solution:

Concept:

Let the numerator be

x

, so denominator is

x + 7

. Adding

2

to denominator gives a new fraction equal to

\frac{4}{7}

.

Explanation:

Original fraction:

\frac{x}{x+7}

.

After adding

2

to denominator:

\frac{x}{x+7+2} = \frac{x}{x+9}

.

Given:

\frac{x}{x+9} = \frac{4}{7}

.

Cross-multiply:

7x = 4(x+9)

.

Simplify:

7x = 4x + 36

→

3x = 36

→

x = 12

.

Denominator:

12 + 7 = 19

.

Thus, the fraction is

\frac{12}{19}

.

Answer:

\frac{12}{19}

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