SSC CGL 2024 Tier-I · 19 September 2024, Shift 3 · Quantitative Aptitude · Question 7 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.

A class of 30 students appeared in a test. The average score of 12 students is 62, and that of the rest is 68. What is the average score of the class?

(a)66.6
(b)63.6
(c)65.6
(d)64.6

Answer

Why

Correct — C. The class is 30, so "the rest" is 30 − 12 = 18 students.

Total of the first group = 12 × 62 = 744
Total of the rest = 18 × 68 = 1224
Class total = 744 + 1224 = 1968

Class average = 1968 ÷ 30 = 65.6 → option (c).

Sanity check: 65.6 lies between 62 and 68 and nearer to 68, which is right when 18 of the 30 students are in the 68 group.

Why the others are wrong

(a)
66.6 — 66.6 needs a class total of 66.6 × 30 = 1998. The two groups supply 744 + 1224 = 1968, thirty marks short of that.
(b)
63.6 — 63.6 lies below 65, the midpoint of 62 and 68. The larger group of 18 is the one averaging 68, so the class figure has to sit above that midpoint.
(d)
64.6 — 64.6 falls on the wrong side of the same midpoint. It would need a class total of 1938 rather than the 1968 the two groups actually produce.

Concept

A combined average is a weighted mean: multiply each group's average by its size, add the two totals, then divide by the total number of students.

Averaging 62 and 68 to 65 would only be right if the groups were equal, and here they are 12 against 18. The weights also decide which side of 65 the answer falls on — with the bigger group scoring 68, the class average must be above 65.

The stem gives the size of only one group. The other is 30 − 12, and picking it up is half the work of the question.

Key facts

Combined average = (n₁a₁ + n₂a₂) ÷ (n₁ + n₂).
Here 12 × 62 + 18 × 68 = 1968, and 1968 ÷ 30 = 65.6.
A combined average always lies between the two group averages.
It lies nearer the average of the larger group, so 65.6 sits closer to 68 than to 62.

Study next

Finding a missing group size when the combined average is givenAlligation, which reads the same weighted mean as a ratio of distancesAverage after a correction, where one wrongly recorded score is replaced

Common traps

Averaging 62 and 68 to get 65, which holds only for equal-sized groups
Treating "the rest" as another 30 students rather than the remaining 18
Marking an option below 65 when the larger group has the higher average

SSC reuses this sentence with a different second average: 11 Sep 2024, 16:00, Quant Q.9 uses 74, 13 Sep 2024, 16:00, Quant Q.8 uses 72, 23 Sep 2024, 16:00, Quant Q.10 uses 60 and 24 Sep 2024, 16:00, Quant Q.18 uses 78.

The 12-of-30 split holds in each of those four, so the working never changes. At 25 Sep 2024, 16:00, Quant Q.20 both averages move instead, to 60 and 80.

Related PYQs

No directly related past PYQ was found.