SSC CGL 2024 Tier-I · 24 September 2024, Shift 1 · Quantitative Aptitude · Question 12 of 98

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, 80% of the voters cast their votes, out of which 4% votes were declared invalid. A candidate got 15,360 votes which were 80% of the valid votes. Find the total number of votes.

(a)18,000
(b)23,000
(c)25,000
(d)20,000

Answer

Why

Correct — C. Work backwards from the 15,360 votes, undoing one percentage at a time.

15,360 is 80% of the valid votes:
valid = 15,360 ⁄ 0.8 = 19,200

Valid votes are 100% − 4% = 96% of the votes cast:
cast = 19,200 ⁄ 0.96 = 20,000

Votes cast are 80% of the total:
total = 20,000 ⁄ 0.8 = 25,000 → option (c).

Why the others are wrong

(a)
18,000 — 18,000 is smaller than the 20,000 votes actually cast. The total electorate cannot be fewer than the people who turned out, so this fails on sight.
(b)
23,000 — 23,000 does not reproduce the chain: 23,000 × 0.8 × 0.96 × 0.8 = 14,131, not the 15,360 votes the candidate got.
(d)
20,000 — 20,000 is the number of votes cast, the second step, not the total. The stem asks for the total number of votes, one division further back.

Concept

Three percentages sit in a chain here, and each is taken on a different base.

Turnout is a share of the total. Invalid votes are a share of what was cast. The candidate's share is taken on the valid votes.

Written forward the chain is total × 0.80 × 0.96 × 0.80 = 15,360. When the last number is the one you are given, you divide back along the same chain instead of multiplying.

Naming the base at every step is the whole discipline: 80% of what, 4% of what.

The two 80% figures are deliberately the same number on different bases — turnout, and the winner's share of valid votes. Nothing in the question links them.

Key facts

Invalid votes are counted out of the votes cast, so valid votes are 96% of the polled votes here.
A candidate's percentage is quoted against valid votes: 15,360 = 0.80 × valid.
Chained percentages multiply: 25,000 × 0.80 × 0.96 × 0.80 = 15,360.
To undo a percentage chain, divide by each factor in reverse order.

Study next

Working backwards through chained percentages by dividingMajority and margin problems where the winner's share is givenSuccessive discounts, which multiply the same way

Common traps

Stopping at 20,000, the votes cast, when the total is asked
Taking the 4% invalid off the total electorate instead of off the votes cast
Treating the two 80% figures as the same quantity

The template repeats with the numbers changed: 85% turnout, 2% invalid and the winner on 78% of valid votes at 10 Sep 2024, 16:00, Quant Q.10, and 80% turnout with 5% invalid at 17 Sep 2024, 12:30, Quant Q.22.

Related PYQs

No directly related past PYQ was found.

Topic: Percentage — all 51 SSC CGL questions on it, every solved shift.