Question

Mukesh’s present age is three times his son’s present age and two-fifth of his father’s present age. The average of the present ages of all of them is 46 years. What is the difference between Mukesh’s son’s present age and Mukesh’s father’s present age?

• A. 68 years
• B. 88 years
• C. 58 years
• D. Cannot be determined
• E. None of these

Answer 1

The correct option is E

None of these

Let the present age of Mukesh’s son be x years. So present age of Mukesh = 3x years.

Given that Mukesh’s present age is two-fifth of his father’s present age.

$\frac{2}{5}$ of present age of Mukesh’s father = Mukesh’s present age

So, present age of Mukesh’s father

$=\frac{5}{2}$ of Mukesh’s present age $=\frac{5}{2}\times 3x=\frac{15x}{2}$

Also given that the average of the present ages of all of them is 46 years

$\therefore \frac{x+3x+\frac{15x}{2}}{3}=46$

Or $\frac{2x+6x+15x}{2}=138$

Or $23x=276$

x = present age of Mukesh’s son = 12

And present age of Mukesh’s father $=\frac{15}{2}\times 12=90$

Therefore the difference between the Mukesh’s son’s present age and Mukesh’s father’s present age = 90 - 12 = 78