JAMB 2013 Mathematics · Question 43
P varies jointly as m and u, and varies inversely as q. Given that p = 4, m = 3 and u = 2 and q = 1, find the value of p when m = 6, u = 4 and q =
Options
- A.12
- B.15
- C.10
- D.28
Answer: C. 10
Explanation written with AI and checked against the answer key
Analyze the question: P varies jointly as m and u (so P grows with both) and inversely as q (so P shrinks as q grows). We need the constant of variation first, then use it to find the new P. Concept: P = k·m·u / q Step 1: Find k Given p = 4, m = 3, u = 2, q = 1: 4 = k(3)(2)/1 4 = 6k k = 2/3 Step 2: Find p for the new values m = 6, u = 4, q = 8/5: p = (2/3)(6)(4) / (8/5) p = (2/3)(24) / (8/5) p = 16 / (8/5) p = 16 × 5/8 p = 10 (Options A and D are written oddly, as mixed numbers with 8/5, but they don't match our working anyway.) Answer: C (10) Tip: For joint and inverse variation problems, always write one equation like P = kmu/q first, find k, and substitute. A quick shortcut is to use ratios: m doubles (×2), u doubles (×2), and q goes from 1 to 8/5, so p becomes 4 × 2 × 2 ÷ (8/5) = 16 × 5/8 = 10.AI can make mistakes. Report anything that looks wrong.
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