CAT 2020 Question Paper | Quants Slot 3

CAT Previous Year Paper | CAT Quants Questions | Question 6

This question is from Linear Equations, with one layer of Arithmetic added on top of it. Being good at framing equations comes in handy during your CAT Preparation. This topic also helps you in other chapters. This question talks about three brothers. Their ages have been given following a particular relation. We need to find the age of one of these three brothers.

Question 6 : 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


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Explanatory Answer

Let's consider Tom's age to be 'x' years.

Dick is thrice as old as Tom,
Dick's age = 3 × x = 3x

Harry is twice as old as Dick,
Harry's age = 2 × 3x = 6x

Dick's age is 1 year less than the average age of all three,
3x = Average(x, 3x, 6x) - 1
3x = \\frac{x+3x+6x}{3}) - 1
3x = \\frac{10x}{3}) - 1
1 = \\frac{10x}{3}) - 3x
1 = \\frac{10x - 9x}{3})
1 = \\frac{x}{3})
3 = x
x = 3

Harry's age = 6x = 6 × 3 = 18 years.


The question is "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"

Hence, the answer is, "18"

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