SSC CGL 2025 Tier-I · 18 September 2025, Shift 2 · Quantitative Aptitude · Question 19 of 100

We transcribed this text from the pictures on a candidate's response sheet for this shift; the answer is the key SSC colour-marked on that sheet. Solution last reviewed 11 September 2026.

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In a trapezoid, the two parallel sides are in the ratio 3:5. If the height of the trapezoid is 10 cm and its total area is 240 cm², determine the lengths of the parallel sides.

(a)15 cm and 25 cm
(b)18 cm and 30 cm
(c)20 cm and 40 cm
(d)30 cm and 50 cm

Answer

Why

Correct — B. Turn the ratio into lengths with one unknown, then use the trapezium area formula.

Sides in the ratio 3:5: 3k and 5k
Area = ½ × (sum of parallel sides) × height
Substitute: 240 = ½ × (3k + 5k) × 10

Simplify the right side: ½ × 8k × 10 = 40k
Solve 40k = 240: k = 6
Sides: 3 × 6 = 18 cm and 5 × 6 = 30 cm

Check the area: ½ × (18 + 30) × 10 = 240 cm² → option (b)

Why the others are wrong

(a)
15 cm and 25 cm — 15 and 25 keep the 3:5 ratio but give the wrong area: ½ × (15 + 25) × 10 = 200 cm², not 240 cm².
(c)
20 cm and 40 cm — 20 : 40 is 1 : 2, not 3 : 5, so it fails the ratio before the area is checked. Its area would also be wrong: ½ × 60 × 10 = 300 cm².
(d)
30 cm and 50 cm — 30 and 50 are in the ratio 3:5 but give too much area: ½ × (30 + 50) × 10 = 400 cm². That is k = 10, not k = 6.

Concept

A trapezium's area is ½ × (sum of the parallel sides) × height: the average of the two parallel sides times the distance between them.

When the sides are given only as a ratio, turn it into lengths with one multiplier, so 3:5 becomes 3k and 5k. The area equation then has a single unknown, and each option can be tested twice: once for the ratio, once for the area.

The paper says trapezoid, the American name. NCERT textbooks call the same figure, a quadrilateral with one pair of parallel sides, a trapezium.

Key facts

Area of a trapezium = ½ × (a + b) × h, where a and b are the parallel sides and h is the perpendicular distance between them.
A ratio p : q of unknown size is written as pk and qk before it goes into a formula.
Here k = 6: the sides 18 cm and 30 cm average 24 cm, and 24 × 10 = 240 cm².

Study next

Finding the height of a trapezium from its area and parallel sidesArea of a trapezium given all four sides, by splitting it into a rectangle and trianglesRatio-to-k substitution in rectangle and triangle area problems

Common traps

Picking 15 cm and 25 cm because the 3:5 ratio fits, without checking the area.
Dropping the ½: (3k + 5k) × 10 = 240 gives k = 3 and sides of 9 cm and 15 cm.

The ratio-to-k step also opens 21 Sep 2025, 16:00, Quant Q.11: legs in the ratio 5:12 with a 13 m hypotenuse give 5k, 12k and 13k with k = 1, so the area is ½ × 5 × 12 = 30 m².

Related PYQs

No directly related past PYQ was found.

Topic: Ratio & Proportion — all 64 SSC CGL questions on it, every solved shift.