Question

Ten years ago, the ratio of the ages of a father and his son was 5:3. Five years from now, the ratio of their respective ages
will be 3:2. Find the sum of their present ages.​

Answer 1

Solution :

Ten years ago, the ratio of the ages of a father and his son was 5:3.

Let their ages at that time be 5x and 3x years respectively .

Five years from now , that is after 15 years ;

The ratio of their respective ages is 3 : 2

> [ 5x + 15 ]/[ 3x + 15 ] = 3 : 2

> 2 [ 5x + 15] = 3[ 3x + 15]

> 10x + 30 = 9x + 45

> x = 15

Age Of Father then :

> 5x = 75 years

Are of son then :

. 3x = 45 years

Present age of father and son are 85 years and 55 years .

The sum of their present ages is 140 years.

This is the required answer .

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Answer 2

Answer:

Given :-

• Ten years ago the ratio of the ages of a father and his son is 5 : 3. Five years ago, the ratio of their respective ages will be 3 : 2.

To Find :-

• What are their present ages.

Solution :-

Let, the present age of father be 5x

And, the present age of son will be 3x

According to the question,

⇒ $\sf\dfrac{5x + 15}{3x + 15} =\: \dfrac{3}{2}$

By doing cross multiplication we get,

⇒ $\sf 2(5x + 15) =\: 3(3x + 15)$

⇒ $\sf 10x + 30 =\: 9x + 45$

⇒ $\sf 10x - 9x =\: 45 - 30$

➠ $\sf\bold{\red{x =\: 15\: years}}$

Hence, the required ages are,

✧ Present age of father = 5x = 5(15) = 75 years

✧ Present age of son = 3x = 3(15) = 45 years

$\therefore$ The present age of father is 75 years and the present age of son is 45 years.