SSC CGL 2025 Tier-I · 19 September 2025, Shift 1 · Quantitative Aptitude · Question 12 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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The sides of a rectangular prism are in the ratio 4:5:6. If the volume of the prism is 960 cm³ what is the length of its longest side?

(a)12 cm
(b)10 cm
(c)8 cm
(d)16 cm

Answer

Why

Correct — A.
Let the sides be 4x, 5x and 6x.
Volume: 4x × 5x × 6x = 120x³ = 960
Divide by 120: x³ = 8, so x = 2

Longest side = 6x = 6 × 2 = 12 cm → option (a).
Check: 8 × 10 × 12 = 960 cm³.

Why the others are wrong

(b)
10 cm — 10 cm is 5x, the middle side. The question asks for the longest side, which is 6x = 12 cm.
(c)
8 cm — 8 cm is 4x, the shortest side. It is also the value of x³, so stopping one step early lands here too.
(d)
16 cm — 16 cm is none of the sides 8, 10 and 12. A longest side of 16 needs x = 8⁄3, and then the volume is about 2275.6 cm³, not 960.

Concept

When sides come only as a ratio, write them as multiples of one unknown: 4x, 5x, 6x. The volume becomes a single term, 120x³, and one division plus one cube root recovers x.

Every side follows from x, so check which side the question wants before you multiply.

A rectangular prism is the same solid as a cuboid: three pairs of rectangular faces, with volume = length × breadth × height.

Key facts

Volume of a cuboid (rectangular prism) = length × breadth × height.
Sides in the ratio p : q : r can be written px, qx and rx, giving volume pqr·x³.
Here 4 × 5 × 6 = 120, so 120x³ = 960 gives x = 2 and sides of 8, 10 and 12 cm.

Study next

Total surface area of a cuboid from a side ratio: 2(lb + bh + hl)Space diagonal of a cuboid: √(l² + b² + h²)Cuboids given as a ratio plus one side, asking for the volume

Common traps

Stopping at x = 2 or x³ = 8 instead of multiplying by 6
Picking the middle term of the ratio instead of the largest

24 Sep 2024, 16:00, Quant Q.17 runs the ratio method the other way: sides 3 : 2 : 1 with breadth 12 cm give x = 6, sides 18, 12 and 6, and a volume keyed 1296 cm³.

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 51 SSC CGL questions on it, every solved shift.