Question

Chagan was solving a math’s problem, “When Tom was born, his father Tony’s age was 30 years older than his sister Sara and his mother Marry was 20 years older than this brother Sam. Sara is 4 years elder than Sam. After 2 years, the average age of Tom’s family is 20. Find the age of Marry when Tom was born?” He is even unable to understand the problem, help him to find out Marry’s age.
1. 30 years
2. 32 years
3. 28 years
4. 38 years

Answer 1

Correct Answer - Option 3 : 28 years

Given∶

Tony’s age was 30 years older than his sister Sara.

Mother Marry was 20 years older than this brother Sam.

Sara is 4 years elder than Sam.

After 2 years, the average age of Tom’s family is 20.

Formula Used∶

Concept of Average, Linear Equations.

Calculation∶

Let the present age of Sam be ‘x’ years

Then, Sara’s age = (x + 4) years

Tony’s age = 30 + x + 4 = (x + 34) years

Marry’s age = (20 + x) years

So, the sum of their ages = x + x + 4 + x + 34 + 20 + x = 4x + 58

After 2 years, the sum of their ages will increased by 2 × 5 = 10 years

∴ The sum of their ages after 2 years = 4x + 58 + 10 = (4x + 68) years    ----(1)

Also, The average age of 5 members of Tom’s family = 20

So, Sum of their ages = 20 × 5 = 100 (2)

On equating eq. (1) and (2), we get

4x + 68 = 100

⇒ 4x = 32

⇒ x = 8

Marry’s age = 20 + x = 20 + 8 = 28 years.

∴ When Tom was born, Marry’s age was of 28 years.