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p varies directly as the square of q and inversely as r. If p =...

Mathematics
JAMB 1984

p varies directly as the square of q and inversely as r. If p = 36, when q = 3, when r = 4, find p when q = 5 and r = 2.

  • A. 72
  • B. 100
  • C. 90
  • D. 200
  • E. 125
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Correct Answer: Option D
Explanation

P \(\alpha\) \(\frac{q^2}{r}\)

P = \(\frac{kq^2}{r}\)

k = \(\frac{pr}{q^2}\)

= \(\frac{36 x 4}{(3)^2}\)

p = \(\frac{16q^2}{r}\)

= \(\frac{16 \times 25}{2}\)

= 200


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