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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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" **

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