Quantitative Reasoning

Linear Equation

Easy

The present ratio of ages of P and Q is 2:7. Six years ago, this ratio was 1:5. Determine the present age of P?

12 years

56 years

15 years

16 years

✅ Correct Option: 4

The present ratio of ages of P and Q is 2:7.

Let P's present age = $2x$ and Q's present age = $7x$

Six years ago:

P's age = $2x - 6$

Q's age = $7x - 6$

The ratio 6 years ago was 1:5, so:

$\frac{2x - 6}{7x - 6} = \frac{1}{5}$

$5(2x - 6) = 1(7x - 6)$

$10x - 30 = 7x - 6$

$10x - 7x = -6 + 30$

$3x = 24$

$x = 8$

P's present age = $2x$

P's present age = $2 \times 8$

P's present age = $16$ years

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Solution

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