Question

Average age of a father and his son is 22 years. Ratio of their age is 10 : 1, what is the age of the son?(a) 24 years
(b) 4 years(c) 40 years(d) 6 years

Answer 1

Let their ages be x and y .

( x + y )/2 = 22

⇒ x + y = 22 × 2

⇒ x + y = 44

Ratio of age = 10 : 1

⇒ x : y = 10 : 1

⇒ x / y  = 10

⇒ x = 10 y

Put this in the original equation :

10 y + y = 44

⇒ 11 y = 44

⇒ y = 44/11

⇒ y = 4

ANSWER :

OPTION B

Answer 2

Answer:

The age of the son be 4 years.

Explanation:

Given,

Average age of father and his son = 22 years

Ratio of their ages = 10: 1

Let the father’s age be x and the son’s age be y

Then, their average be

$\frac {(x+y)}{2}=22\\\\x+y=22\times2\\\\x+y=44$

Thus, the sum of their ages be 44

Given, their ratios be 10: 1

Thus,  

$10x+1x=44\\\\11x=44\\\\x=4$

Thus, the father’s age be $10x=10\times4=40$ years

The son’s age be $1x=1\times4=4$ years

Hence, the age of the son be 4 years. Thus, the correct answer is (b) 4 years.