NECO 2005 Mathematics · Question 2

T varies directly as D and inversely as A. Given that T = 6, D = 3, and A = 2, find A when T = 3 and D = 6.

Options

A.4
B.6
C.8
D.12
E.24

Answer: C. 8

Explanation written with AI and checked against the answer key

Analyze the question: T varies directly as D and inversely as A. This is a combined (joint) variation problem. Concept: If T varies directly as D and inversely as A, then T = kD/A, where k is a constant. Step 1: Find k Using T = 6, D = 3, A = 2: 6 = k(3)/2 6 = 3k/2 k = (6 × 2)/3 = 4 Step 2: Write the formula T = 4D/A Step 3: Find A when T = 3 and D = 6 3 = 4(6)/A 3 = 24/A A = 24/3 = 8 Check: T = 4(6)/8 = 24/8 = 3 ✓ Answer: A = 8, which is option C. Tip: For combined variation, write the full formula T = kD/A first, then find k using the first set of values. Always substitute back to check your answer. Direct variation goes on top (numerator), inverse variation goes on the bottom (denominator).

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