SSC CGL 2024 Tier-I · 18 September 2024, Shift 2 · Quantitative Aptitude · Question 19 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.

The average weight of 10 students is increased by half a kg when one of the students weighing 51 kg is replaced by a new student. Find the weight of the new student.

(a)45 kg
(b)56 kg
(c)66 kg
(d)75 kg

Answer

Why

Correct — B. Replacing one student changes the total, and the average only tracks the total.

Rise in the average = 0.5 kg across 10 students
Rise in the total = 10 × 0.5 = 5 kg

That entire 5 kg comes from the swap, so the newcomer is 5 kg heavier than the student who left.
51 + 5 = 56 kg → option (b)

The other nine weights, and the original average itself, are never needed.

Why the others are wrong

(a)
45 kg — Option (a), 45 kg, is lighter than the 51 kg student who left. A lighter replacement pulls the total down and the average with it, and the average here rose.
(c)
66 kg — Option (c), 66 kg, adds 15 kg to the total. Spread over 10 students that lifts the average by 1.5 kg, not the half kg the question states.
(d)
75 kg — Option (d), 75 kg, adds 24 kg to the total and 2.4 kg to the average, far above the stated half kg.

Concept

An average is a total in disguise. For n items, total = n × average, so any movement in the average costs n times as much at the total.

Replacement problems live on that. When one member leaves and another joins, every other value is untouched, so the whole change in the total is the difference between the two swapped values:

new value − old value = n × change in average

Here 10 × 0.5 = 5, so the new student weighs 51 + 5 = 56 kg. The original average never appears, and it is not needed.

Half a kg is written in words rather than as 0.5, which is where a rushed reader loses the factor of 10. Multiply it by the group size before doing anything else.

Key facts

For n values, total = n × average, so a change of d in the average changes the total by n × d.
In a replacement, new value = old value + n × (change in the average).
Here the total rises by 10 × 0.5 = 5 kg, so the new student weighs 51 + 5 = 56 kg.
A replacement that lowers the average means the incoming value is smaller than the one removed.

Study next

Replacement problems where a member leaves and another joins a fixed-size groupWeighted averages combining two groups of different sizesRecovering a missing value from a stated change in the average

Common traps

Adding the half kg straight to 51 and answering 51.5 kg.
Subtracting instead of adding, which gives 46 kg for what is a rise in the average.
Hunting for the original average, which the question never supplies and does not need.

SSC sets averages as a change to a total rather than a fresh mean. At 09 Sep 2024, 12:30, Quant Q.9 the overlap between two sixteen-day temperature averages fixes the reading on the sixteenth day, and at 12 Sep 2024, 09:00, Quant Q.11 the average of twelve numbers is split across groups to recover the last few.

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