Question

The denominator of a fraction exceeds the numerator by 5. If 3 be added to both, the fraction becomes 3/4. Find the fraction.

Answer 1

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Answer 2

Given:

The denominator of a fraction exceeds the numerator by 5. If 3 be added to both, the fraction becomes 3/4.

To find:

The fraction.

Solution:

First of all, we should know that in a fraction a/b, the a is called the numerator while b is called the denominator.

Now,

let the numerator of a given fraction be x.

So,

according to the question,

denominator = x + 5.

So, the fraction is

$\frac{x}{x + 5}$

Now,

as given,

If 3 be added to both, the fraction becomes 3/4.

So, we have,

$\frac{x + 3}{x + 5 + 3} = \frac{3}{4}$

On solving above, we have,

$\frac{x + 3}{x + 8} = \frac{3}{4}$

After cross multiplication, we have,

$4x + 12 = 3x + 24$

$x = 12$

So,

denominator is

$= x + 5 = 12 + 5 = 17$

Hence, the required fraction is 12/17.