SSC CGL 2024 Tier-I · 19 September 2024, Shift 3 · Quantitative Aptitude · Question 24 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.

Three candidates X, Y and Z participated in an election. X got 30% more votes than Y, whereas Z got 25% more votes than Y. X also overtook Z by 5000 votes. If 71% of the voters voted and no invalid votes were cast, then what was the total number of voters in the voting list?

(a)5,00,000
(b)4,50,000
(c)3,55,000
(d)4,05,000

Answer

Why

Correct — A. Both comparisons are made against Y, so make Y the base.

Let Y = y. Then X = 1.30y and Z = 1.25y.
X − Z = 0.05y = 5,000 → y = 1,00,000

Votes cast = X + Y + Z = (1.30 + 1 + 1.25)y = 3.55 × 1,00,000 = 3,55,000

Those votes are 71% of the list, and none were invalid:
Total voters = 3,55,000 ⁄ 0.71 = 5,00,000 → option (a)

Why the others are wrong

(b)
4,50,000 — 4,50,000 voters would put a 71% turnout at 3,19,500 votes, but the three candidates polled 3,55,000 between them.
(c)
3,55,000 — 3,55,000 is the number of votes cast — the answer one step early. The question asks for the voting list, of which those votes are 71%.
(d)
4,05,000 — 4,05,000 × 0.71 = 2,87,550 votes, well short of the 3,55,000 actually polled by X, Y and Z.

Concept

Two percentages are quoted against Y and one against the electoral roll, so the whole question is about keeping the bases apart.

Against Y: X = 1.30y, Z = 1.25y, and the 5,000-vote lead is the gap 1.30y − 1.25y = 0.05y. Five per cent of y being 5,000 gives y = 1,00,000 in one division.

Against the roll: X + Y + Z = 3.55y = 3,55,000 votes were cast, and with no invalid votes those are exactly the 71% who turned out. Dividing by 0.71 recovers the roll.

The phrase no invalid votes were cast is what lets votes cast and votes counted be the same number. When SSC adds an invalid-vote percentage, one more multiplication sits between turnout and the candidates' totals.

Key facts

X = 1.30Y and Z = 1.25Y, so X's lead over Z is 5% of Y's votes.
5% of Y = 5,000 gives Y = 1,00,000 and X + Y + Z = 3.55 × 1,00,000 = 3,55,000.
A 71% turnout with no invalid votes means 3,55,000 = 0.71 × total voters.
3,55,000 ⁄ 0.71 = 5,00,000, the number of names on the voting list.

Study next

Choosing as the algebraic base the quantity everything else is compared againstThe turnout chain: voting list, votes cast, valid votes, a candidate's shareMajority questions where the winning margin is a percentage of the valid votes

Common traps

Reading Z's 25% as 25% more than X rather than 25% more than Y.
Stopping at 3,55,000, the votes cast, when the question asks for the list.
Taking X's 5,000 lead as a lead over Y, which would make the gap 0.30y.

The turnout half is asked on its own at 17 Sep 2024, 12:30, Quant Q.22, where 80% of voters vote, 5% of the polled votes are invalid and a 36,480 majority fixes 1,20,000 voters.

The comparison half — one candidate polling a stated percentage of another's votes and winning by a fixed number — is at 13 Sep 2024, 09:00, Quant Q.12, keyed 16,170.

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