SSC CGL 2024 Tier-I · 9 September 2024, Shift 2 · Quantitative Aptitude · Question 6 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 5 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.

Seven years ago, Prachi was four times as old as her daughter was at that time. Four years from now, Prachi will be two-and-a-half times as old as her daughter would then be. Find the sum of the present ages (in years) of Prachi and her daughter.

(a)77
(b)49
(c)72
(d)69

Answer

Why

Correct — D. Let Prachi be P and her daughter D today, and shift both by the same number of years in each clause.

Seven years ago: P − 7 = 4(D − 7)
→ P = 4D − 21

Four years from now: P + 4 = 2.5(D + 4)
Substitute P = 4D − 21:
4D − 17 = 2.5D + 10
1.5D = 27 → D = 18

P = 4(18) − 21 = 51
Sum of present ages = 51 + 18 = 69 → option (d)

Check: 44 = 4 × 11, and 55 = 2.5 × 22.

Why the others are wrong

(a)
77 — 77 is the sum four years from now, 55 + 22. Both equations are written in shifted ages, so it is easy to stop there — the question asks for present ages.
(b)
49 — 49 comes from applying the 2.5 ratio to present ages: P = 2.5D with P − 7 = 4(D − 7) gives D = 14 and P = 35. The ratio holds four years from now, not today.
(c)
72 — 72 is 4 × 18 — the daughter's present age times the ratio that applied seven years ago, when they were 11 and 44. The question asks for a sum, not a multiple.

Concept

An age problem is two linear equations in two unknowns, and the only real skill is shifting both people by the same amount before comparing them.

Write today's ages as P and D. 'Seven years ago' becomes P − 7 and D − 7; 'four years from now' becomes P + 4 and D + 4.

Because both move together, their difference never changes — here Prachi is 33 years older than her daughter at every moment in the problem, which is often the fastest check on a candidate answer.

'Two-and-a-half times as old' means 2.5 multiplied, not two and a half years more. The misreading is common under time pressure.

Clearing the fraction turns the second equation into 2P + 8 = 5D + 20, which some candidates find safer to solve than decimals.

Key facts

The gap between two people's ages never changes.
Prachi is 33 years older than her daughter at every point in this problem.
'Seven years ago' subtracts 7 from both ages, and 'four years from now' adds 4 to both.
The present ages are 51 and 18, and they satisfy both clauses: 44 = 4 × 11 and 55 = 2.5 × 22.

Study next

Three-person age problems where the third relation is a stated total rather than a ratioRatio-form questions such as 'their ages are 4:1 now and 5:2 in six years'Using the constant age difference to eliminate a variable and solve in one step

Common traps

Shifting only one person's age by the given number of years.
Answering a single age, or the future sum, when the question asks for the present sum.
Reading 'two-and-a-half times as old' as an addition rather than a multiple.

SSC fixes two clauses at different points in time and then asks for one age, the sum, the difference, or a ratio at a third time. Quant Q.11 of this same paper is the three-person version — A, B and C with a stated total — and asks for a ratio spanning five years back and three years forward.

Related PYQs

No directly related past PYQ was found.