SSC CGL 2024 Tier-I · 19 September 2024, Shift 1 · Quantitative Aptitude · Question 3 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.

In a family, the combined age of husband, wife and a son is 90 years. The husband is the oldest. The difference in the ages of the husband and wife is 1⁄3 rd the age of their son. After 10 years, the age of the son would be half the age of his father. What is the present age of his mother (in years)?

(a)40
(b)45
(c)35
(d)30

Answer

Why

Correct — C. Three conditions, three unknowns — H (husband), W (wife), S (son).

H + W + S = 90
H − W = S ⁄ 3
After 10 years: H + 10 = 2(S + 10) → H = 2S + 10

Substitute W = 90 − H − S into the second line:
2H + S − 90 = S ⁄ 3 → H + S ⁄ 3 = 45

(2S + 10) + S ⁄ 3 = 45 → 7S ⁄ 3 = 35 → S = 15
H = 40, so W = 90 − 40 − 15 = 35 years → option (c)

Why the others are wrong

(a)
40 — 40 is the husband's age, which the working produces on the way. The question asks for the mother, so this is the right arithmetic answering the wrong person.
(b)
45 — 45 is half of the 90-year total. No condition splits the family in two, and it also happens to be the intermediate value of H + S ⁄ 3, which is not anyone's age.
(d)
30 — 30 is the equal three-way split of 90. It fails the second condition at once: equal ages make H − W = 0, while S ⁄ 3 would be 10.

Concept

Age questions are linear equations with the story stripped off. Name one variable per person and turn each sentence into a line.

The clause that carries the most weight here is the future one: after 10 years, add 10 to every age, so H + 10 = 2(S + 10). Candidates who add 10 to one side only lose the question here.

Three independent equations settle three unknowns, so no guessing is needed; the ages are H = 40, W = 35 and S = 15.

The stem says 'the husband is the oldest', which is a consistency check rather than a fourth equation — 40 > 35 > 15 satisfies it. The answer asked for is the mother's age, that is, the wife's.

Key facts

Adding a fixed number of years changes every age in the problem by that same amount.
The solution set here is husband 40, wife 35 and son 15, totalling 90.
Check the future clause: in 10 years the son is 25 and the father is 50, exactly half.

Study next

Age problems mixing a past condition with a future one in the same stemSolving three linear equations by substitution rather than eliminationRatio-form age questions where the ratio changes after n years

Common traps

Ageing only one person in the future condition.
Reading one-third of the son's age as one-third of the total instead.
Answering with the husband's 40 when the mother's age was asked.

SSC hides the person actually asked for in the final line, after several sentences about someone else. The same build-and-substitute routine solves the marble question at Quant Q.7 in this shift.

Related PYQs

No directly related past PYQ was found.