NECO 2001 Mathematics · Question 8

If t varies inversely as the cube of s, and t = 24, when s = 3, find t when s = 2

Options

A.8
B.24
C.27
D.81
E.648

Answer: D. 81

Explanation written with AI and checked against the answer key

Analyze the question: t varies inversely as the cube of s, so t = k/s³. Concept: In inverse variation, find the constant k from the given pair of values, then use it to find the unknown. Solution: Step 1: Find k using t = 24 when s = 3. 24 = k/3³ = k/27 k = 24 × 27 = 648 Step 2: Find t when s = 2. t = 648/2³ = 648/8 = 81 Check with a shortcut: t₁s₁³ = t₂s₂³ 24 × 27 = t × 8 t = 648/8 = 81 ✓ Tip: For "inversely as the cube," the product t × s³ stays constant. You can skip finding k and just write t₂ = t₁ × (s₁/s₂)³ = 24 × (3/2)³ = 24 × 27/8 = 81. Since s decreased, t must increase. That is a quick way to catch mistakes (for example, option A would be wrong because it is smaller than 24).

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