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Age ratio problem

CAT 2020 Slot 3 · Quantitative Ability · Easy · Ratios and proportions

This is an easy Quantitative Ability question from the CAT 2020 Slot 3 paper. It tests Ratios and proportions. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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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

Answer

18

Explanation

Let Tom's age be tt. Dick's age D=3tD = 3t. Harry's age H=2D=6tH = 2D = 6t.

Average age of all three = t+3t+6t3=10t3\frac{t + 3t + 6t}{3} = \frac{10t}{3}. Given: D=10t3−1D = \frac{10t}{3} - 1 3t=10t3−1  ⟹  t3=1  ⟹  t=33t = \frac{10t}{3} - 1 \implies \frac{t}{3} = 1 \implies t = 3.

Harry's age H=6t=18H = 6t = 18 years.

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