SSC CGL 2025 Tier-I · 21 September 2025, Shift 1 · Quantitative Aptitude · Question 8 of 99

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 13 September 2026.

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SSC does not publish CGL question papers or a public answer key. From 2025 the candidate response sheet prints every question and option as a picture, so the text here is transcribed from those pictures for this shift and checked against them independently; where the layout carries meaning, the picture is shown as well. Each answer is the key SSC colour-marked on that sheet. SSC released a tentative key for challenge and later its final one, both only to candidates behind a login, and the sheet does not say which of the two it carries. The solutions are written by UnlockIAS.

A company designs a new chocolate box in the shape of a regular right pyramid with a square base. The base side of the box is 10 cm and its height is 12 cm. Due to packaging constraints, the box can only be filled up to 90% of its total volume. If the company wants to estimate the total cost of chocolate, knowing that 1 cm³ of chocolate costs ₹0.50, what is the cost of chocolate to fill one such box?

(a)₹180
(b)₹225
(c)₹270
(d)₹300

Answer

Why

Correct — A. Volume of a pyramid = ⅓ × base area × height.

Base area = 10 × 10 = 100 cm²
Full volume = ⅓ × 100 × 12 = 400 cm³
Filled to 90% = 0.9 × 400 = 360 cm³

Cost = 360 × ₹0.50 = ₹180 → option (a)

Why the others are wrong

(b)
₹225 — ₹225 buys 225 ÷ 0.50 = 450 cm³ of chocolate. The full box holds only 400 cm³, and just 360 cm³ can go in.
(c)
₹270 — ₹270 is what ½ in place of ⅓ gives: ½ × 100 × 12 = 600 cm³, 90% of that is 540 cm³, and 540 × ₹0.50 = ₹270.
(d)
₹300 — ₹300 pays for 600 cm³, which is ½ × 100 × 12 with no 90% cut. The whole box holds only 400 cm³.

Concept

A pyramid holds exactly one third of the prism on the same base and height. A 10 × 10 × 12 cuboid holds 1200 cm³, so the pyramid holds 400 cm³.

After that the 90% limit and the price per cm³ are plain percentage and rate steps. Stay in cm³ until the last line, then convert to rupees once.

The slant height, √(5² + 12²) = 13 cm, is not needed. Volume uses the vertical height, which the question gives as 12 cm.

Key facts

Volume of a pyramid = ⅓ × base area × vertical height.
A pyramid holds one third of the prism with the same base and height.
For this square pyramid (base 10 cm, height 12 cm) the slant height is √(5² + 12²) = 13 cm.

Study next

Lateral and total surface area of a square pyramid, which use the slant heightVolume of a cone, ⅓πr²h, the same one-third rule on a circular baseVolume of a frustum of a pyramid or cone

Common traps

Using ½ instead of ⅓ in the volume formula, which turns ₹180 into ₹270.
Putting the slant height (13 cm) in place of the vertical height (12 cm).

The ⅓ rule is asked bare at 15 Sep 2025, 09:00, Quant Q.17 (base area 60 cm², height 9 cm, volume 180 cm³).

A square base given by its diagonal comes up in Tier-II Paper-I, 19 Jan 2026, 11:00, Quant Q.24 (diagonal √512 m, height 8 m, about 683 m³).

Related PYQs

No directly related past PYQ was found.

Topic: Right Prism, Right Circular Cone, Right Circular Cylinder, Sphere, Hemispheres, Rectangular Parallelepiped, Regular Right Pyramid with triangular or square base — all 99 SSC CGL questions on it, every solved shift.