SSC CGL 2024 Tier-I · 17 September 2024, Shift 2 · Quantitative Aptitude · Question 22 of 100

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.

Two candidates contested in an election. 80% of the voters cast their votes, out of which 5% of the polled votes were invalid. The winning candidate got 70% of valid votes and won by a majority of 36,480 votes. Find the total number of voters.

(a)1,18,000
(b)1,15,000
(c)1,20,000
(d)1,25,000

Answer

Why

Correct — C. Let the total number of voters be V and apply the percentages one layer at a time.

Votes polled = 80% of V = 0.80 V
Valid votes = 95% of the polled votes = 0.95 × 0.80 V = 0.76 V

Winner 70%, loser 30%, so the majority is 40% of the valid votes.
Majority = 0.40 × 0.76 V = 0.304 V

0.304 V = 36,480
V = 36,480 ⁄ 0.304 = 1,20,000 → option (c).

Why the others are wrong

(a)
1,18,000 — 1,18,000 voters would produce a majority of 0.304 × 1,18,000 = 35,872 votes, which falls 608 short of the 36,480 the stem states.
(b)
1,15,000 — 1,15,000 yields 0.304 × 1,15,000 = 34,960, a shortfall of 1,520 votes. Nothing in the chain of filters can make up that gap.
(d)
1,25,000 — 1,25,000 yields 0.304 × 1,25,000 = 38,000, overshooting the stated majority by 1,520 votes.

Concept

An election percentage stem is a chain of filters, each applied to whatever survived the previous one.

Total voters → those who polled (80%) → those whose votes were valid (95% of the polled) → the split between the two candidates (70 : 30).

The fact that decides the item is that the majority is the winner's share minus the loser's, that is 70% − 30% = 40% of the valid votes, not 70% of them.

Multiply the three fractions in order — 0.80 × 0.95 × 0.40 = 0.304 — and the whole chain collapses into one number.

There are only two candidates. That is what lets you write the loser's share as 100% − 70%, and it is why the majority is 40% of the valid votes.

Put a third candidate on the ballot and the same arithmetic breaks, because the runner-up's share would no longer be the remainder.

Key facts

Between two candidates, majority = (winner's % − loser's %) of the valid votes.
Invalid votes are counted out of the votes polled, not out of the total electorate.
Here 0.80 × 0.95 × 0.40 = 0.304, so the majority is 30.4% of the total number of voters.
36,480 ⁄ 0.304 = 1,20,000 voters.

Study next

Chained percentage filters where each rate applies to the previous survivorRecovering the electorate from a stated majority rather than from a raw vote countThree-candidate election stems, where the loser's share is no longer the remainder

Common traps

Taking the 5% invalid votes out of the total voters instead of out of the votes polled
Using the winner's 70% as the majority instead of the 40% difference
Answering with the number of valid votes when the stem asks for the number of voters

SSC stacks two or three filters — turnout, invalid votes, then the winner's share — and asks for whichever quantity is left out.

A heavier version with a 42 : 58 split and a 45,360 majority runs at 23 Sep 2024, 12:30, Quant Q.25. A stripped-down one that states all polled votes are valid is at 18 Sep 2024, 12:30, Quant Q.17.

Related PYQs

No directly related past PYQ was found.