GATE 2024 EC GA Q.3: solution and answer

GATE 2024 · ECGA Q.3 · 1 mark · MCQ

Five years ago, the ratio of Aman's age to his father's age was 1:4, and five years from now, the ratio will be 2:5. What was his father's age when Aman was born?

(A)
28 years
(B)
30 years
(C)
35 years
(D)
32 years

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Answer and solution

ANSWER

The father was 30 years old when Aman was born. The answer is (B).

Official answer: BSource: Official answer key, GATE 2024 EC (IISc Bengaluru)

Let Aman's and his father's ages five years ago be $x$ and $4 x$ , which gives the ratio $1 : 4$ .
Five years from now is 10 years after that point, so their ages will then be $x + 10$ and $4 x + 10$ .
Set up the second ratio: $\frac{x + 10}{4 x + 10} = \frac{2}{5}$
Cross-multiply: $5 (x + 10) = 2 (4 x + 10) \Rightarrow 5 x + 50 = 8 x + 20 \Rightarrow 3 x = 30 \Rightarrow x = 10$ .
Their present ages are $10 + 5 = 15 years$ (Aman) and $40 + 5 = 45 years$ (father). Check: in five years they will be $20$ and $50$ , and $20 : 50 = 2 : 5$ .
The gap between two people's ages never changes, so the father's age when Aman was born equals that gap: $45 - 15 = 30 years$ . Using the ages five years ago gives the same answer: $4 x - x = 3 x = 30 years$ . The answer is (B).

KEY IDEA

Put one variable on the earlier ratio ( $x$ and $4 x$ five years ago), shift both ages by the same 10 years to reach the later ratio, and solve. The father's age when the son was born is just the age gap, which stays the same over time: $4 x - x = 3 x$ .

WATCH OUT FOR

Adding only 5 years (instead of 10) to the 'five years ago' ages when writing the 'five years from now' ratio. Another common slip is answering with the father's present age (45) or his age five years ago (40) instead of the age gap (30).

From the GATE 2024 EC paper. Every question of this paper · Download the full paper · All 58 Numerical questions, with notes

GATE 2024 EC GA Q.3: solution and answer

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