SSC CGL 2024 Tier-I · 25 September 2024, Shift 1 · Quantitative Aptitude · Question 15 of 100

Text as printed on a candidate's response sheet for this shift; answer per SSC's tentative key as marked on that sheet. Solution last reviewed 10 September 2026.

Where this paper and its answers come from

SSC does not publish CGL question papers or a public answer key. The questions and options here are reproduced as printed on a candidate's own response sheet for this shift — the Commission's text, unchanged. Each answer is SSC's tentative key as marked on that sheet; SSC allowed challenges to it and never publishes a final key. The solutions are written by UnlockIAS.

Nihira is 25 years old and Punith is 30 years old. How many years ago was the ratio of their ages 3 : 4?

(a)10 years
(b)15 years
(c)5 years
(d)20 years

Answer

Why

Correct — A. Take the same number of years off both ages and set the ratio.

Let it be x years ago: (25 − x) ⁄ (30 − x) = 3⁄4
Cross-multiply: 4(25 − x) = 3(30 − x)
100 − 4x = 90 − 3x
10 = x → 10 years ago, option (a)

Verify: ten years back they were 15 and 20, and 15 : 20 = 3 : 4.

Faster, without algebra: the gap between them is always 5 years, and 4 − 3 = 1 part, so one part is 5. The ages were 3 × 5 = 15 and 4 × 5 = 20 — ten years before 25 and 30.

Why the others are wrong

(b)
15 years — Taken as an elapsed time, 15 years back makes them 10 and 15, a 2 : 3 ratio. Fifteen is tempting because it is Nihira's age at the moment the 3 : 4 held — the age, not the gap.
(c)
5 years — 5 years back they were 20 and 25, which is 4 : 5. Halving the correct shift leaves the ratio short of 3 : 4, because the gap of 5 is then more than one part.
(d)
20 years — 20 years back they were 5 and 10, a 1 : 2 ratio. The further back you go, the more the fixed 5-year gap dominates, so the ratio moves away from 3 : 4, not towards it.

Concept

Ages move together. Subtract the same x from both, and the difference between them never changes — here it is 5 years, today and at every point in the past.

That is what makes the shortcut work. If the ages were once in the ratio 3 : 4, the parts differ by 4 − 3 = 1, and that one part has to equal the fixed gap of 5.

So the ages then were 15 and 20, and 25 − 15 = 10 years have passed.

The algebra reaches the same place; the shortcut just skips the cross-multiplication.

The question asks how many years ago, not what the ages were.

Both 10 and 15 are true numbers in this problem — 10 is the elapsed time and 15 was Nihira's age — and only one of them answers what was asked.

Key facts

The difference between two people's ages is constant over time.
For a ratio a : b with a constant difference d, one part equals d ⁄ (b − a).
Here d = 5 and b − a = 1, so one part is 5 and the ages were 15 and 20.
15 : 20 reduces to 3 : 4, confirming 10 years ago.

Study next

Age problems giving a present ratio plus a past or future ratio, solved with one variableAge problems where the sum of the ages is given alongside a ratioUsing the constant-difference shortcut on any ratio pair whose difference is fixed

Common traps

Subtracting x from one age only
Answering with the age at that time rather than the elapsed years
Cross-multiplying the wrong way and getting 3(25 − x) = 4(30 − x), which gives x = 45

SSC hands you both present ages here, leaving the time shift as the single unknown.

The harder build keeps one age hidden behind a second ratio, as at 18 Sep 2024, 12:30, Quant Q.22, where a present ratio of 3 : 4 and a five-years-back ratio of 2 : 3 have to be solved together, and at 23 Sep 2024, 16:00, Quant Q.12, which spans three years back and thirteen years forward.

Related PYQs

No directly related past PYQ was found.