Question

A family consists of three sons and
their parents. Average age of the
family is 20 years. Average of the ages
of second eldest son and parents is 24
years. Difference between parents age
together and second eldest son is 48
years. Ratio of ages of second eldest
son and eldest son is 2:3 What is the
age of the youngest son?​

Answer 1

Answer:

Youngest son age = 10 years

Answer 2

Answer:

The age of the youngest son is 10 years.

Step-by-step explanation:

Let the age of eldest son be a, second eldest son be b and the third eldest son be c. Let the age of parents be p.

Average age of family = 20

(a + b + c + p) / 5 = 20  ( we have taken 5 as parents include 2 persons.)

a + b + c + p = 100 ...(1)

Also,

Average of the ages

of second eldest son and parents = 24

(b + p) / 3  =24

b + p = 72 ...(2)

Also, the difference between parents age together and second eldest son is 48 years that is:

p - b = 48 ...(3)

p = 48 + b

Put in (2)

48 + b + b = 72

2 b = 24

b = 12  ...(4)

p = 48 + b = 48 + 12 = 60   ...(5)

Ratio of ages of second eldest son and eldest son is 2:3

b : a = 2 : 3

b / a = 2 / 3

From (4), we get that:

12 / a = 2 / 3

2a = 36

a = 18 ...(6)

Put (4), (5) and (6) in (1):

a + b + c + p = 100

18 + 12 + c + 60 = 100

90 + c = 100

c = 100 - 90

c = 10.

Therefore, the age of the youngest son is 10 years.

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