SSC CGL 2024 Tier-I · 25 September 2024, Shift 3 · Quantitative Aptitude · Question 4 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 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.

The ratio of circumference and diameter of a circle is 3 : 5. If the circumference is 6 cm, then the radius of the circle is:

(a)1.8 cm
(b)10 cm
(c)15 cm
(d)5 cm

Answer

Why

Correct — D. The stem supplies the ratio circumference : diameter = 3 : 5, so the diameter is 5⁄3 of the circumference.

d = C × 5⁄3
= 6 × 5⁄3 = 10 cm
r = d ⁄ 2 = 10 ⁄ 2 = 5 cm → option (d)

Read the ratio in the order it is written: the 3 belongs to the circumference, which is the quantity you were given, so it goes underneath.

Why the others are wrong

(a)
1.8 cm — 1.8 cm is the ratio inverted. Taking d = 6 × 3⁄5 = 3.6 cm gives r = 1.8 cm, but then C : d would be 6 : 3.6 = 5 : 3, which is the stem's ratio backwards.
(b)
10 cm — 10 cm is the diameter, not the radius — the working stops one step early. The question asks for the radius, which is half of it.
(c)
15 cm — 15 cm as the radius means a diameter of 30 cm, so C : d would be 6 : 30 = 1 : 5. The stem fixes that ratio at 3 : 5.

Concept

This is ratio arithmetic wearing a geometry costume. A ratio a : b between two quantities lets you convert either into the other by multiplying by b⁄a or a⁄b — the whole question is choosing the right one.

C : d = 3 : 5 means d = C × 5⁄3. With C = 6 cm that gives d = 10 cm.

Only the last step is geometric, and it is the definition rather than a formula: the radius is half the diameter.

Be clear about what the stem asks you to accept. For a genuine circle, circumference ÷ diameter is π ≈ 3.1416, so a ratio of 3 : 5 = 0.6 cannot describe one, and no real circle has a diameter longer than its circumference.

The item is therefore impossible as geometry and only works as ratio arithmetic. Following the ratio the paper supplies gives 5 cm, which is what SSC's key marks, so that is what this card explains.

Key facts

C : d = 3 : 5 with C = 6 cm gives d = 6 × 5⁄3 = 10 cm.
Radius = diameter ⁄ 2, so r = 5 cm.
Inverting a given ratio swaps the multiplier b⁄a for a⁄b, which here is the difference between 10 cm and 3.6 cm.
For any real circle, circumference ÷ diameter equals π ≈ 3.1416 — the value this stem replaces with 0.6.

Study next

Rearranging C = 2πr and A = πr² to get the radius from either measurementRatio-of-radii questions, where circumferences scale as r and areas as r²Reading the order of a stated ratio, which decides whether you multiply or divide

Common traps

Answering 10 cm, the diameter, because it appears as an option.
Multiplying by 3⁄5 rather than 5⁄3 and landing on 1.8 cm.
Discarding the given ratio in favour of C = πd, which the stem's own numbers contradict.

SSC dresses ratio conversion as mensuration so the candidate reaches for a formula instead of the given proportion. Circumference is also the working quantity at 25 Sep 2024, 12:30, Quant Q.15, where one circle's circumference equals the sum of two others.

Related PYQs

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