SSC CGL 2024 Tier-I · 24 September 2024, Shift 3 · Quantitative Aptitude · Question 18 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 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.

A class of 30 students appeared in a test. The average score of 12 students is 62, and that of the rest is 78. What is the average score of the class?

(a)69.6
(b)71.6
(c)70.6
(d)72.6

Answer

Why

Correct — B. "The rest" is 30 − 12 = 18 students, and they carry the heavier weight.

Total of the first group = 12 × 62 = 744
Total of the rest = 18 × 78 = 1404
Combined total = 744 + 1404 = 2148

Class average = 2148 ⁄ 30 = 71.6 → option (b).

Why the others are wrong

(a)
69.6 — The larger group — 18 of the 30 — is the one scoring 78, so the class average must sit above the plain midpoint of 62 and 78, which is 70. 69.6 is below it and cannot be reached.
(c)
70.6 — 70.6 needs a class total of 70.6 × 30 = 2118, but the two groups actually add to 2148. It falls exactly one mark per student short.
(d)
72.6 — 72.6 needs a total of 72.6 × 30 = 2178, which is 30 marks above the real 2148 — one mark per student too many.

Concept

A combined average is a weighted average. You cannot average the two group averages; you must rebuild each group's total, add them, and divide by the whole head-count.

The word doing the work is rest. It means the students not already counted, so 30 − 12 = 18, and the 78-scoring group is one and a half times the size of the 62-scoring one.

That is why the answer 71.6 sits above 70: the mean is pulled towards the average of the bigger group. A combined average always lands strictly between the two group averages, never outside them.

Every option lies between 62 and 78, so the usual sanity check of "is it inside the range?" eliminates none of them here — the arithmetic has to be done.

Key facts

Combined average = (sum of all group totals) ÷ (sum of all group sizes).
The plain mean of 62 and 78 is 70, while the true class average here is 71.6.
A two-group combined average always lies strictly between the two group averages.
Group total = group size × group average, which is how you convert an average back into marks.

Study next

Weighted average when three or more groups are combinedRecovering a missing group average from the combined averageAlligation as a one-line shortcut for two-group averages

Common traps

Averaging 62 and 78 to 70 and picking the nearest option.
Swapping the weights, so 62 gets 18 students and 78 gets 12, which gives 68.4.
Treating "the rest" as all 30 students instead of the 18 not yet counted.

SSC reuses this exact stem with the numbers changed — the same 30-student, 12-scoring-62 setup is asked at 11 Sep 2024, 09:00, Quant Q.2 (where the rest also score 62) and at 11 Sep 2024, 16:00, Quant Q.9 (where the rest score 74).

Related PYQs

No directly related past PYQ was found.