SSC CGL 2024 Tier-I · 13 September 2024, Shift 2 · Quantitative Aptitude · Question 2 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.

P and Q are two fixed points 10 cm apart, and R is a point on PQ such that PR = 6 cm. By what percentage is the length of QR decreased when the length of PR is increased by 5%?

(a)7%
(b)8.5%
(c)7.5%
(d)8%

Answer

Why

Correct — C. P and Q are fixed, so PQ stays 10 cm throughout and whatever PR gains, QR loses.

QR = 10 − 6 = 4 cm

PR after a 5% rise = 6 × 1.05 = 6.3 cm (5% is charged on PR's own 6 cm)
New QR = 10 − 6.3 = 3.7 cm

Decrease in QR = 4 − 3.7 = 0.3 cm
Percentage decrease = 0.3⁄4 × 100 = 7.5% → option (c)

Why the others are wrong

(a)
7% — 7% would mean QR fell by 0.28 cm. PR rises by 5% of its own 6 cm, which is 0.30 cm exactly, and every millimetre of it comes out of QR.
(b)
8.5% — No step here produces 8.5%. The fall is pinned at 0.3 cm and the original QR at 4 cm, so the only defensible ratio is 0.3⁄4.
(d)
8% — 8% is what 0.3⁄3.7 rounds to — dividing by the new QR instead of the original. Percentage change always sits on the starting value, 4 cm.

Concept

Two lengths that must add to a constant do not change by the same percentage.

PR + QR = PQ = 10 cm at every instant, so the absolute changes are equal and opposite: PR up 0.3 cm means QR down 0.3 cm.

The percentages differ because the bases differ. 0.3 on a base of 6 is 5%; the same 0.3 on a base of 4 is 7.5%.

The whole question is a test of which number you divide by, and the smaller a part is, the louder any given absolute change speaks in percentage terms.

R is described as a point on PQ, so PR and QR are the two pieces of a 10 cm segment — there is no third piece to absorb the change.

Key facts

P and Q are fixed, so PR + QR = 10 cm at all times.
A 5% rise on PR is 5% of 6 cm = 0.3 cm, not 5% of the 10 cm segment.
Percentage decrease uses the original QR of 4 cm as its base, giving 0.3⁄4 = 7.5%.

Study next

Percentage change measured against the correct baseComplementary parts of a fixed totalConverting an absolute change into a percentage of the original value

Common traps

Taking 5% of PQ (0.5 cm) rather than 5% of PR.
Dividing the 0.3 cm fall by the new QR of 3.7 cm, which gives about 8.1%.
Assuming QR falls by 5% because PR rose by 5%.

The numbers stay small enough to do in the head and the work hides in the base — the mark goes to whoever notices that the 5% is charged on PR while the answer is asked about QR.

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