SSC CGL 2024 Tier-I · 18 September 2024, Shift 1 · Quantitative Aptitude · Question 21 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 6 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 perimeter of a rectangular garden is 48 m. If the length is 6 m more than the breadth, the area (in m 2 ) of the garden is:

(a)135
(b)84
(c)96
(d)112

Answer

Why

Correct — A. Halve the perimeter first — that single step turns the problem into two easy equations.

2(l + b) = 48 → l + b = 24
Length is 6 m more than breadth → l = b + 6

Substitute: (b + 6) + b = 24 → 2b = 18 → b = 9 m, so l = 15 m.

Area = l × b = 15 × 9 = 135 m² → option (a).

Why the others are wrong

(b)
84 — With l + b = 24 locked by the perimeter, an area of 84 m² would need sides of roughly 4.3 m and 19.7 m — a gap of about 15.5 m, not the 6 m the question states.
(c)
96 — 96 = 12 × 8, a pair that differs by 4 m rather than 6 and adds to 20 m, so its perimeter would be 40 m, not 48 m.
(d)
112 — 112 = 14 × 8, the sharpest decoy here: those sides do differ by 6 m, but they add to 22 m, giving a perimeter of 44 m. The stated 48 m forces l + b = 24.

Concept

A rectangle is pinned down by any two independent facts about its sides. Here the perimeter gives their sum and the wording gives their difference.

Perimeter = 2(l + b), so dividing by 2 is the whole trick: l + b = 24 and l − b = 6.

Sum and difference together give the sides immediately — half-sum plus half-difference is the length, half-sum minus half-difference is the breadth: 12 + 3 = 15 and 12 − 3 = 9.

The paper prints the unit as "in m 2" because the superscript was flattened when the response sheet was rendered. It means square metres.

Key facts

Perimeter of a rectangle = 2(length + breadth), so half the perimeter is length + breadth.
Sides that sum to 24 m and differ by 6 m are exactly 15 m and 9 m.
Area = length × breadth = 15 × 9 = 135 m².
For a fixed perimeter the area is largest when the sides are equal, so 135 m² sits below the 144 m² of a 12 m square.

Study next

Recovering two numbers from their sum and their differenceMaximum area for a fixed rectangular perimeterWord problems where a side is stated as a multiple rather than an excess of the other

Common traps

Using 48 as length + breadth and skipping the division by 2
Adding the 6 m to the length as well, so both sides grow
Stopping at the breadth of 9 m instead of multiplying out the area

SSC runs this idea from both ends — the plain product at 23 Sep 2024, 16:00, Quant Q.8, where length and breadth are handed to you, and this version, where the sides must first be recovered from a perimeter and a difference.

Related PYQs

No directly related past PYQ was found.