Question

The present age of Sharman is twice the sum of the ages of his two sons. Six years ago, his age was 5 times the sum of the ages of two sons. Find the present age of Sharman.

Answer 1

Given:

• Present age of Sharman = (x)
• Present ages of his two sons = (a) and (b)

According to the problem:

1. The present age of Sharman is twice the sum of the ages of his two sons.

x = 2(a + b)

2. Six years ago, Sharman’s age was 5 times the sum of the ages of his two sons.

Six years ago, Sharman’s age = (x – 6)

Six years ago, sum of his sons’ ages

= (a – 6) + (b – 6)

= a + b – 12

According to the problem:

x – 6 = 5(a + b – 12)

Step-wise calculation:

1. From the first equation: 

x = 2(a + b)

⇒ `a + b = x/2`

2. Substitute `(a + b = x/2)` into the second equation:

`x - 6 = 5(x/2 - 12)`

3. Simplify the right-hand side:

`x - 6 = 5 xx x/2 - 5 xx 12`

`x - 6 = (5x)/2 - 60`

4. Multiply both sides by 2 to clear the fraction: 

2x – 12 = 5x – 120

5. Rearranging terms: 

2x – 12 – 5x + 120 = 0 

–3x + 108 = 0 

3x = 108 

x = 36

The present age of Sharman is 36 years.