SSC CGL 2024 Tier-I · 24 September 2024, Shift 3 · Quantitative Aptitude · Question 3 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 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 angles of a triangle are in the ratio 1 : 2 : 3. The difference in the largest and smallest angle is (in degrees):

(a)15
(b)30
(c)45
(d)60

Answer

Why

Correct — D.

Let the angles be x, 2x and 3x.

Angle sum of a triangle: x + 2x + 3x = 180°
6x = 180° → x = 30°

So the angles are 30°, 60° and 90°.

Largest − smallest = 3x − x = 2x
= 2 × 30° = 60° → option (d).

Why the others are wrong

(a)
15 — No two of 30°, 60° and 90° differ by 15°. A gap of 15° would need 2x = 15°, so x = 7.5° and an angle sum of 45°, not 180°.
(b)
30 — 30° is x itself — the smallest angle, and also the step between neighbours (60 − 30 and 90 − 60). The question asks largest minus smallest, which is 3x − x = 2x.
(c)
45 — 45° is not a gap between any two of these angles. 2x = 45° would put x at 22.5° and the angle sum at 135°, and 180° forces x = 30°.

Concept

A ratio fixes proportions only; a second fact fixes the actual size. Here that fact is the angle sum of a triangle, 180°.

Write the parts as x, 2x, 3x, add them to 180°, and one equation settles everything: 6x = 180°, so x = 30°.

The result also tells you the triangle is right-angled, because the largest part, 3 of the 6 ratio parts, is half of 180°. Any 1 : 2 : 3 angle ratio behaves this way.

The question asks for a difference, not for an angle, so the last step is 3x − x rather than 3x.

Key facts

The three angles of a triangle add to 180°, which is what converts a ratio into degrees.
Angles in the ratio 1 : 2 : 3 are 30°, 60° and 90°, so the triangle is right-angled.
For parts x, 2x, 3x the largest-minus-smallest gap is 2x, double the smallest angle.

Study next

Angles in a given ratio with a fixed sum: triangles at 180°, quadrilaterals at 360°Exterior angle theoremRelating the largest angle of a triangle to the longest side

Common traps

Answering with the smallest angle, 30°, instead of the difference.
Dividing 180° by 3 instead of by the 6 ratio parts.
Reading difference as the step between consecutive angles rather than between the extremes.

The same sentence returns with numbers that do not divide as kindly.
12 Sep 2024, 09:00, Quant Q.3 gives the ratio 17 : 13 : 15 and asks for the positive difference between the greatest and the smallest angle; 26 Sep 2024, 09:00, Quant Q.19 gives 7 : 8 : 3 and asks for the largest angle alone.

Related PYQs

No directly related past PYQ was found.