SSC CGL 2025 Tier-I · 12 September 2025, Shift 1 · Quantitative Aptitude · Question 21 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 circular pizza having a radius of 21 cm. If 75% of it is eaten, what is the area of pizza remaining?

(a)173.25 cm²
(b)346.36 cm²
(c)432.25 cm²
(d)115.5 cm²

Answer

Why

Correct — B. Eating 75% leaves 25%, a quarter of the pizza.

Area of the whole pizza = πr² = π × 21² = 441π cm²
Remaining quarter = 441π ÷ 4 = 110.25π cm²
With π ≈ 3.1416: 110.25 × 3.1416 ≈ 346.36 cm² → option (b)

With π = 22⁄7 the same steps give 1386 ÷ 4 = 346.5 cm², and (b) is still the nearest option.

Why the others are wrong

(a)
173.25 cm² — 173.25 is 1386 ÷ 8, one-eighth of the pizza (with π = 22⁄7). That is half of what is left: 12.5% instead of the 25% remaining.
(c)
432.25 cm² — 432.25 cm² is about 31% of the whole pizza (432.25 ÷ 1386 ≈ 0.31). The part left is exactly 25%, which is about 346 cm².
(d)
115.5 cm² — 115.5 is 1386 ÷ 12, one-twelfth of the pizza, about 8.3%. A quarter of the pizza is three times as much.

Concept

The area of a circle is πr², so a fraction of the circle has that same fraction of its area. A pizza with 75% eaten keeps 25%, and 25% of πr² is πr² ÷ 4.

Take the fraction first and multiply by π last: 21² = 441, 441 ÷ 4 = 110.25, and only then × π. That keeps the arithmetic clean and puts the choice of π in a single step.

The stem gives no value of π. The keyed 346.36 comes from π ≈ 3.1416. π = 22⁄7 gives 346.5, which is not printed, and π = 3.14 gives about 346.19.

All three land near 346, and no other option comes close.

Key facts

Area of a circle = πr². For r = 21 cm, r² = 441.
With π = 22⁄7, a circle of radius 21 cm has area 22 × 63 = 1386 cm².
A quarter of a circle is a sector with a 90° central angle and a quarter of the area.

Study next

Area and perimeter of a sector from its central anglePerimeter of the part of a circle left after a sector is removedArea of a ring between two concentric circles

Common traps

Finding the area eaten (75%) instead of the area remaining (25%).
Using the diameter, 42 cm, as the radius, which makes every area four times too large.

The same 21 cm pizza with a quarter removed is on 13 Sep 2024, 09:00, Quant Q.24, but there the question asks for the perimeter of what is left: three-quarters of the 132 cm rim plus two radii, 99 + 42 = 141 cm.

A sector as a fraction of the circle is asked on 17 Sep 2024, 09:00, Quant Q.12: an area of 16π out of 64π is a quarter, a 90° angle.

Related PYQs

No directly related past PYQ was found.

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