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CAT 2020 Slot 3 — QA Question 17

Basics of AverageEasy

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 & solution

Answer: 18

Solution

Easy

Express all three ages in terms of Tom's age, then translate "Dick is 1 year less than the average" into a single equation and solve.

1

Ages in one variable. Let Tom's age be xx.

Tom=x,Dick=3x,Harry=2×3x=6x\begin{aligned} &\text{Tom}=x,\qquad \text{Dick}=3x,\qquad \text{Harry}=2\times 3x=6x \end{aligned}
2

Use the average condition. Dick's age is 11 less than the average of the three.

3x=x+3x+6x3−1⇒ 3x=10x3−1⇒ 9x=10x−3⇒ x=3\begin{aligned} &3x=\frac{x+3x+6x}{3}-1\\ &\Rightarrow\ 3x=\frac{10x}{3}-1\\ &\Rightarrow\ 9x=10x-3\\ &\Rightarrow\ x=3 \end{aligned}
3

Harry's age.

Harry=6x=6×3=18\begin{aligned} &\text{Harry}=6x=6\times 3=18 \end{aligned}
Harry=18 years\text{Harry}=18\ \text{years}
CAT 2020 Slot 3 QA Q17: 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 — Solution | TheCATExam