Question

The numerator and denominator of a fraction are in the ratio 5:7. If the numerator is reduced by 5 and the denominator is increased by 6, the ratio becomes 1:4. Find the fraction.​

Answer 1

To find,

The actual fraction which is in the ratio 5:7

Solution,

For this purpose, we shall consider the fraction to be

$\frac{5x}{7x}$

Given,

Let's subtract five from the numerator. Similarly, let's add six to the denominator.

$\frac{5x - 5 }{7x + 6} = \frac{1}{4}$

Solving for x,

By using cross multiplication we get,

4 (5x - 5) = 1 (7x + 6)

20x - 20 = 7x + 6

13x = 26

x = 2

Hence, the fraction is

$\frac{5 \times 2}{7 \times 2} = \frac{10}{14}$

Therefore, the answer is $\frac{10}{14}$