JAMB 2019 Mathematics · Question 41

If M varies directly as N and inversely as the root of P. Given that M = 3, N = 5 and P = 25. Find the value of P when M = 2 and N = 6.

Options

A.36
B.63
C.47
D.81

Answer: D. 81

Explanation written with AI and checked against the answer key

Step 1: Analyze the question M varies directly as N and inversely as the square root of P, so: M = kN/√P Step 2: Find the constant k Using M = 3, N = 5, P = 25: 3 = k(5)/√25 = 5k/5 = k So k = 3. Step 3: Use k to find P With M = 2, N = 6: 2 = 3(6)/√P 2 = 18/√P √P = 18/2 = 9 P = 81 Step 4: Answer Check: M = 3(6)/√81 = 18/9 = 2 ✓ Exam tip: For variation questions, always follow three steps: write the equation with k, find k from the first set of values, then substitute the second set. "Inversely as the root of P" means P goes under a square root in the denominator. Remember to square at the end, since you solve for √P first.

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