CAT 2020

Slot 3

QA

Question & Solution

1. Concept Used

• Topic: Averages & Linear Equations
• Formula: $$ \text{Average} = \frac{\text{Sum of all values}}{\text{Number of values}} $$

2. Calculation

Let Tom's age $= x$ years.

Since Dick is thrice as old as Tom: $\text{Dick's age} = 3x$

Since Harry is twice as old as Dick: $\text{Harry's age} = 2 \times 3x = 6x$

The average age of all three is: $$\text{Average} = \frac{x + 3x + 6x}{3} = \frac{10x}{3}$$

We are told Dick's age is 1 year less than the average age of all three: $$3x + 1 = \frac{10x}{3}$$

Multiplying both sides by 3: $$9x + 3 = 10x$$

$$x = 3$$

Therefore, Harry's age: $$6x = 6 \times 3 = 18 \text{ years}$$

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3. Solution

Answer = 18 ✅

The final calculated value is 18 years.