SSC CGL 2025 Tier-I · 12 September 2025, Shift 3 · Quantitative Aptitude · Question 8 of 100

We transcribed this text from the pictures on a candidate's response sheet for this shift; the answer is the key SSC colour-marked on that sheet. Solution last reviewed 11 September 2026.

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Three groups of students have average ages 18, 20, and 22 respectively. If the number of students in the three groups is in the ratio 2:3:5, what is the overall average age?

(a)19.6
(b)20.6
(c)15.6
(d)14.6

Answer

Why

Correct — B. Take the ratio parts as group sizes: 2, 3 and 5 students.

Total age = 2 × 18 + 3 × 20 + 5 × 22
= 36 + 60 + 110 = 206
Total students = 2 + 3 + 5 = 10

Overall average = 206 ÷ 10 = 20.6 → option (b)

Why the others are wrong

(a)
19.6 — 19.6 is below 20, the plain mean of 18, 20 and 22. The 22-year group (5 parts) outweighs the 18-year group (2 parts), and both sit 2 from 20, so the mean is pulled above 20.
(c)
15.6 — 15.6 is below 18, the youngest group's average. A weighted average always lies between the lowest and highest group averages, here 18 and 22.
(d)
14.6 — 14.6 is also below 18. Every student belongs to a group whose average is at least 18, so the overall average cannot fall under 18.

Concept

The overall average of several groups is a weighted average: multiply each group's average by its size, add, and divide by the total size.

A ratio of sizes works as well as real counts. Doubling every group doubles both the total age and the number of students, so the average does not change.

The result always lies between the lowest and highest group averages and leans toward the biggest group.

Options (c) and (d) fall below every group's average and go at sight. Between (a) and (b), the direction of the pull decides: the heaviest weight sits on 22.

Key facts

Weighted average = sum of (size × average) ÷ sum of sizes.
Group sizes in the ratio 2 : 3 : 5 can be taken as 2, 3 and 5 students.
A weighted average lies between the lowest and highest group averages, here 18 and 22.

Study next

Finding the ratio of two groups from their averages and the combined averageAverage change when a member joins or leaves a groupWeighted average with group sizes given as percentages

Common traps

Taking the plain mean (18 + 20 + 22) ÷ 3 = 20, which ignores that the 22-year group is the largest.
Dividing 206 by 3, the number of groups, instead of by 10, the number of students.

Here the group sizes come only as a ratio. With actual counts, the same weighted average settles 26 Sep 2024, 09:00, Quant Q.2 (90 boys at 52 kg and 60 girls at 48 kg, 50.4 kg) and 25 Sep 2024, 12:30, Quant Q.1 (10 students averaging 90 and 20 averaging 75, class average 80).

Related PYQs

No directly related past PYQ was found.

Topic: Averages — all 53 SSC CGL questions on it, every solved shift.