CAT 2020 Slot 3 QA Question 11: Dick is thrice as old as Tom and Harry is twice as old as Dick. If Dick's age is 1 year less than the average age of all three, then Harry's age, in years, is

Question

Dick is thrice as old as Tom and Harry is twice as old as Dick. If Dick's age is 1 year less than the average age of all three, then Harry's age, in years, is

Accepted Answer

Let Tom's age be $t$ years.
Dick's age = $3t$
Harry's age = $6t$
$3t = \dfrac{t + 3t + 6t}{3} - 1$
$\Rightarrow 3t + 1 = \dfrac{10t}{3}$
$\Rightarrow 9t + 3 = 10t$
$\Rightarrow t = 3$
Harry's age = $6t = 18$ years
Answer: 18