Question

The ages of Anuj and his daughter are
in the ratio 11 : 3. After 7 years their
ages will be in the ratio 5:2. The
present age difference of Anuj and his
daughter is:​

Answer 1

Given:

The ages of Anuj and his daughter are  in the ratio 11 : 3

After 7 years their  ages will be in the ratio 5:2

To find:

The  present age difference of Anuj and his  daughter is?

Solution:

Let's assume,

"11x" → represents the present age of Anuj

"3x" → represents the present age of his daughter

So, Ages after 7 years will be:

Anuj's age = (11x + 7) years

His daughter's age = (3x + 7) years

It is given that after 7 years the ratio of their ages become 5:2, so we can write an equation as:

$\frac{11x\:+\:7}{3x\:+\:7} = \frac{5}{2}$

$\implies 2(11x\: +\: 7) = 5(3x\:+\:7)$

$\implies 22x\: +\: 14 = 15x\:+\:35$

$\implies 22x\: - 15x = 35 - \: 14$

$\implies 7x = 21$

$\implies \bold{x = 3}$

∴ Anuj's present age = 11x = 11 × 3 = 33 years

and

∴ His daughter's present age = 3x = 3 × 3 = 9 years

Now,

The difference between their present ages will be,

= [Anuj's present age] - [His daughter's present age]

= 33 - 9

= 24 years

Thus, the  difference between the present age of Anuj and his  daughter is → 24 years.

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