SSC CGL 2024 Tier-I · 10 September 2024, Shift 1 · Quantitative Aptitude · Question 11 of 98

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.

The ages of two friends, Ram and Ravi, differ by 7 years. Ram’s mother Mayadevi is three times as old as Ram, and Ravi is four times as old as his brother Soham. The ages of Mayadevi and Soham differ by 65 years. Find the age of Mayadevi (in years).

(a)45
(b)69
(c)36
(d)85

Answer

Why

Correct — B. Let Ram be R years old, so his mother Mayadevi is 3R.

The two friends differ by 7 years. Take Ravi = R − 7, which makes Soham = Ravi ⁄ 4 = (R − 7)⁄4.

The one number given is Mayadevi − Soham = 65:
3R − (R − 7)⁄4 = 65
(12R − R + 7)⁄4 = 65 → 11R + 7 = 260 → R = 23

Mayadevi = 3 × 23 = 69 → option (b).

The other reading, Ravi = R + 7, gives 11R − 7 = 260 and R = 267⁄11, not a whole number.

Why the others are wrong

(a)
45 — 45 makes Ram 15, Ravi 8 and Soham 2, so Mayadevi and Soham differ by 45 − 2 = 43, not the 65 the question fixes.
(c)
36 — 36 makes Ram 12 and Ravi 5, so Soham would be 5⁄4 = 1.25 years old. The gap 36 − 1.25 = 34.75 also misses 65.
(d)
85 — 85 is not a multiple of 3, so Ram would be 85⁄3 years old. Mayadevi is three times Ram, which forces her age to divide by 3.

Concept

Every relation in this stem is a multiple or a fixed difference, so a single unknown can carry all four people. Name the person the most relations hang off — Ram, because Mayadevi is defined from him and Ravi is only seven years away — and the rest become expressions in R.

The equation itself comes from the one numerical gap you are handed, Mayadevi − Soham = 65. Multiplying through by 4 clears the fraction and keeps the arithmetic in whole numbers.

"Differ by 7 years" does not say who is older, so there are two candidate equations rather than one. Only the branch with Ram as the elder returns whole ages, which is how the question resolves the ambiguity.

Key facts

Mayadevi is three times Ram, so her age must be a multiple of 3.
Ravi is four times Soham, so Ravi's age must be a multiple of 4.
Ram 23, Ravi 16, Soham 4 and Mayadevi 69 satisfy every condition, and 69 − 4 = 65.
Multiplying 3R − (R − 7)⁄4 = 65 by 4 gives 11R + 7 = 260.

Study next

Age problems that fix a ratio at two different points in timeTurning a "differs by" statement into a pair of candidate equationsUsing the divisibility of the options to shortcut an age equation

Common traps

Taking Ravi as the elder, which produces a fractional age and no valid option.
Reading the relation backwards and making Soham four times Ravi.
Solving for Ram and stopping at 23 when the question asks for Mayadevi.

Every relation in this stem is a multiple or a fixed difference, so one unknown can carry all four people and the work sits in the translation rather than the algebra.

SSC also builds age items on ratios taken at two different moments: 9 Sep 2024, 12:30, Quant Q.11 asks for the ratio of B's age five years ago to A's age three years from now, and 23 Sep 2024, 16:00, Quant Q.12 fixes a ratio three years ago and another thirteen years hence.

Related PYQs

No directly related past PYQ was found.