Question

if ratio of mohan’s age to that of his father is 1 : 5. after 10 years, their ages will be in the ratio of 1 : 3. what is the father’s present age?

Answer 1

Present ages of Mohan and his father be x years and 5x years respectively.

Then,    x  + 10      =   1

           5x  + 10          3

3x + 30 = 5x + 10

2x = 20

x = 10

Father's present age = 5x = 50

Answer 2

Solution -

Let the present age of Mohana be x years

So, the present age of her Father be 5x years

After 10 years -

Mohana's age = x + 10 years

Her Father's age = 5x + 10 years

According to Question,

$\Rightarrow \frac{x + 10}{5x + 10} =\frac{1}{3} \quad \text{[By transposition]}\\ \\ \Rightarrow 3(x + 10) = 1(5x + 10) \\ \\ \Rightarrow 3x + 30 = 5x + 10 \\ \\ \Rightarrow 30 - 10 = 5x - 3x \\ \\ \Rightarrow 20 = 2x \qquad \quad\text{[By transposition]} \\ \\ \Rightarrow \frac{20}{2} = x \\ \\ \Rightarrow 10 = x$

Required Ages -

Mohana = x = 10 years

Her Father = 5x = 5(10) = 50 years

Hence, the present age of Mohana is 10 years and her father is 50 years

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