SSC CGL 2024 Tier-I · 19 September 2024, Shift 2 · Quantitative Aptitude · Question 23 of 99

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 6 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 sum of the ages of 6 children born at the interval of two years each is 90 years. What is the age (in years) of the eldest child?

(a)10
(b)16
(c)14
(d)20

Answer

Why

Correct — D. Six children born two years apart give six ages in arithmetic progression with common difference 2.

Let the youngest be a. The ages are a, a+2, a+4, a+6, a+8, a+10.
Sum = 6a + (2 + 4 + 6 + 8 + 10) = 6a + 30

6a + 30 = 90
6a = 60, so a = 10

Eldest = a + 10 = 20 → option (d)
Check: 10 + 12 + 14 + 16 + 18 + 20 = 90.

Why the others are wrong

(a)
10 — 10 is the youngest child, the a of the working. The question asks for the top of the list, not the bottom.
(b)
16 — An eldest of 16 puts the youngest at 6, and 6 + 8 + 10 + 12 + 14 + 16 = 66, not the 90 the stem gives.
(c)
14 — An eldest of 14 puts the youngest at 4, and those six ages total 54 — far short of 90.

Concept

The sum of an arithmetic progression is the number of terms times the average of the first and last, so the mean age here is 90 ÷ 6 = 15.

With an even count the mean falls midway between the third and fourth child, so the six ages are 15 ± 1, 15 ± 3 and 15 ± 5. That reads off as 10, 12, 14, 16, 18 and 20 without an equation, and the eldest is 20.

The stem says the interval is two years each, so consecutive ages differ by 2 and the eldest and youngest are ten years apart, not twelve — five gaps between six children.

Key facts

Sum of an AP = number of terms × average of the first and last term.
Six children two years apart span five gaps, so eldest − youngest = 10 years.
The mean age is 90 ÷ 6 = 15, and the eldest lies 5 years above the mean.
The six ages are 10, 12, 14, 16, 18 and 20.

Study next

Sum of an AP through the n/2 × (first + last) formAge problems given as a ratio now and after a stated number of yearsFinding the middle term when an odd count of equally spaced values is given

Common traps

Answering 10, the youngest age, because it is the a the working solves for.
Counting six gaps instead of five and spreading the ages over 12 years.
Writing the sum as 6a + 2 × 6 by multiplying the interval by the number of children.

Ages come up in this same paper at Quant Q.6, which sets a person's age three years ago against his younger brother's, then adds a second condition eight years ahead — a pair of linear equations to be solved together.

Here the spacing carries the information instead, so an AP sum settles it faster than unknowns would.

Related PYQs

No directly related past PYQ was found.