SSC CGL 2024 Tier-I · 24 September 2024, Shift 2 · Quantitative Aptitude · Question 10 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 radii of two circles are 8 cm and 15 cm.The perimeter of the circle having area equal to the sum of the areas of the two circles (in cm) is:

Answer

Why

Correct — B. Areas add here, radii do not.

Sum of areas = π(8²) + π(15²)
= π(64 + 225) = 289π
Set πR² = 289π → R² = 289 → R = 17 cm

Perimeter = 2πR = 2π × 17 = 34π

The four options are printed as images. The one reading 34π is option (b).

Why the others are wrong

(a)
Option (a) reads 32π, which needs R = 16. Squaring and adding gives 64 + 225 = 289, and √289 is 17, not 16.
(c)
Option (c) reads 28π, so R = 14 — smaller than the 15 cm circle you started with. A circle holding the area of both cannot be smaller than either of them.
(d)
Option (d) reads 30π, which is 2π × 15: the perimeter of the larger circle alone. It throws the 8 cm circle's area away.

Concept

The two circles are being merged by area, not by radius. Adding the radii would build a circle of area π(23)², far more than the two together.

The rule that does work is R² = r₁² + r₂², because area goes as the square of the radius.

Here 8² + 15² = 289 = 17², so the merged circle has radius 17 cm. Only then do you switch formulas and use 2πR for the perimeter.

The stem describes an area condition and then asks for a perimeter, and the two steps use different formulas. Getting R = 17 is most of the work, but 17 is not the answer — 2 × 17 = 34 is.

Key facts

The area of a circle is πr², so merging two circles by area gives R² = r₁² + r₂².
The perimeter (circumference) of a circle of radius R is 2πR.
8, 15, 17 is a Pythagorean triple, which is why √(8² + 15²) lands on the whole number 17.

Study next

Combining circles by area against combining them by circumferencePythagorean triples worth memorising: 3-4-5, 5-12-13, 8-15-17, 7-24-25Arc length and sector area as fractions of 2πR and πR²

Common traps

Adding the radii to get 23 cm instead of adding the areas.
Answering 289π, which is the area, when the question asks for the perimeter.
Reaching R = 17 and stopping, forgetting the factor 2 in 2πR.

Circles come back in different guises. Quant Q.7 of this same shift asks for the chord of the larger of two concentric circles that is tangent to the smaller, and 17 Sep 2024, 09:00, Quant Q.24 asks at what angle an arc is half the perimeter of its circle.

Related PYQs

No directly related past PYQ was found.