SSC CGL 2024 Tier-I · 11 September 2024, Shift 1 · Quantitative Aptitude · Question 13 of 95

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.

In an election between two candidates P and Q, P got 78% of the total valid votes. If the total votes of the electorate were 75,60,000, then what was the number of valid votes that Q got if 10% of the voters did not cast their vote and 15% of the votes polled were declared invalid?

(a)12,72,348
(b)1,47,312
(c)1,41,732
(d)1,41,372

Answer

Why

Correct — A. Work down the chain in the order the question sets it out.

Electorate = 75,60,000
10% did not vote, so votes polled = 90% of 75,60,000 = 68,04,000
15% of the polled votes were invalid, so valid votes = 85% of 68,04,000 = 57,83,400

P took 78% of the valid votes, so Q took the remaining 22%.
Q's votes = 0.22 × 57,83,400 = 12,72,348 → option (a)

In one line: 0.9 × 0.85 × 0.22 × 75,60,000 = 12,72,348.

Why the others are wrong

(b)
1,47,312 — 1,47,312 implies a valid-vote pool of 6,69,600, since 1,47,312 ⁄ 0.22 = 6,69,600. The chain produces 57,83,400 valid votes, and no step produces 6,69,600.
(c)
1,41,732 — This is 1,41,372 with two digits transposed, a proof-reading decoy. It is not 22% of 57,83,400 nor of any figure the percentages generate.
(d)
1,41,372 — The 10% slip: using the 10% who stayed home as the turnout gives 7,56,000 polled, 6,42,600 valid and 1,41,372 for Q. The 10% is the share that did not vote.

Concept

An election question is a chain of percentages, each taken of the line above it, never of the electorate.

Electorate → votes polled (turnout) → valid votes (100% minus the invalid share, applied to the polled votes) → each candidate's share, applied to the valid votes.

Here that is 75,60,000 → 68,04,000 → 57,83,400 → 22% of it. Multiplying the factors in one go is faster: 0.9 × 0.85 × 0.22 = 0.1683, so Q's votes are 16.83% of the electorate.

Only two candidates stand, and invalid votes are already out of the pool, so P's 78% and Q's share must add to 100% of the valid votes. That is what fixes Q at 22%.

Key facts

Votes polled = electorate × turnout, so 90% of 75,60,000 = 68,04,000.
The invalid share is taken of the votes polled, not of the electorate.
Valid votes = 85% of 68,04,000 = 57,83,400.
0.9 × 0.85 × 0.22 = 0.1683, and 16.83% of 75,60,000 is 12,72,348.

Study next

Successive percentages multiplied as decimal factorsWinning margin and majority questions on a valid-vote baseWorking backwards from a margin to the electorate

Common traps

Taking the 15% invalid off the electorate instead of off the votes polled.
Using the 10% who abstained as the turnout, which lands exactly on 1,41,372.
Reporting P's 78% share when the question asks for Q's.

The same chain — turnout, then invalid votes, then a candidate's share — runs at 09 Sep 2024, 09:00, Quant Q.12, where the abstaining share is the unknown.

At 17 Sep 2024, 12:30, Quant Q.22 and 23 Sep 2024, 12:30, Quant Q.25 a winning margin is given and the electorate is what you must find. Spot which link is missing before you start.

Related PYQs

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