SSC CGL 2025 Tier-I · 12 September 2025, Shift 1 · Quantitative Aptitude · Question 23 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 11 September 2026.

Where this paper and its answers come from

SSC does not publish CGL question papers or a public answer key. From 2025 the candidate response sheet prints every question and option as a picture, so the text here is transcribed from those pictures for this shift and checked against them independently; where the layout carries meaning, the picture is shown as well. Each answer is the key SSC colour-marked on that sheet. SSC released a tentative key for challenge and later its final one, both only to candidates behind a login, and the sheet does not say which of the two it carries. The solutions are written by UnlockIAS.

A bicycle wheel having a radius of 35 cm. What percentage of its circumference is covered in a quarter turn?( Use π=22⁄7)

(a)15%
(b)25%
(c)30%
(d)35%

Answer

Why

Correct — B. One full turn of a wheel rolls out one full circumference. A quarter turn rolls out a quarter of it.

Circumference = 2πr = 2 × 22⁄7 × 35 = 220 cm
Quarter turn = 220 ÷ 4 = 55 cm
Percentage = 55 ÷ 220 × 100 = 25% → option (b)

The radius cancels: a quarter of any circumference is 25%.

Why the others are wrong

(a)
15% — 15% of a turn is 0.15 × 360° = 54°, well short of a quarter turn's 90°. On this wheel it would cover 33 cm, not 55 cm.
(c)
30% — 30% of a turn is 108°, more than the 90° of a quarter turn. It would roll out 66 cm of the 220 cm rim, not 55 cm.
(d)
35% — 35 is the radius in centimetres, not a percentage. The share of the rim covered depends only on the fraction of a turn, and a quarter is 25% for any radius.

Concept

A wheel rolling without slipping moves forward by the length of rim that touches the ground. One turn = one circumference, 2πr.

A fraction of a turn covers the same fraction of the circumference. A quarter turn is 90° of 360°, so it covers 1⁄4 = 25%.

The radius and π matter only when the question asks for a distance in centimetres. For a percentage of the circumference they cancel.

The radius (35 cm) and π = 22⁄7 in the stem play no part in the percentage. They give the distance: 220 cm a full turn and 55 cm a quarter turn.

Key facts

Distance covered in one revolution = circumference = 2πr.
A wheel of radius 35 cm has circumference 2 × 22⁄7 × 35 = 220 cm.
A quarter turn is 90°, which is 25% of a full turn and of the circumference.

Study next

Number of revolutions a wheel makes to cover a given distanceArc length of a sector: (θ ÷ 360°) × 2πrA circle whose circumference equals the sum of two given circumferences

Common traps

Reaching for the radius because it is printed, when the percentage of a circumference depends only on the fraction of a turn.

Circumference grows in step with the radius on 25 Sep 2024, 12:30, Quant Q.15: circles of radii 12 and 16 cm together match one of radius 28 cm, a diameter of 56 cm.

A fraction of a rim is part of 13 Sep 2024, 09:00, Quant Q.24, where three-quarters of a 132 cm pizza rim is 99 cm.

Related PYQs

No directly related past PYQ was found.

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