Question

6. (a) Two positive whole numbers P and q are such that P is greater than q and their sum is equal to three times their difference.
(i) Express P in terms of q. (ii) Hence, evaluate (P²+q²)/(Pq).
(b) A man sold 100 articles at 25 for ₦66.00 and made a gain of 32%. Calculate his gain or loss percent if he sold them at 20 for ₦50.00.

Accepted Answer

(a)(i) P+q = 3(P−q) ⇒ P+q = 3P−3q ⇒ 4q = 2P ⇒ P = 2q.
(ii) (P²+q²)/(Pq) = ((2q)²+q²)/(2q×q) = (4q²+q²)/(2q²) = 5q²/2q² = 5/2.

(b) 25 articles sell for ₦66.00, so 1 article = ₦66/25 = ₦2.64; 100 articles sell for ₦264.00 at this rate, which represents S.P at a 32% gain. So C.P for 100 articles = S.P/1.32 = 264/1.32 = ₦200.00.
Now selling 100 articles at 20 for ₦50.00: 1 article = ₦50/20 = ₦2.50; 100 articles = ₦250.00 (new S.P).
Since new S.P (₦250) > C.P (₦200), there's a gain. Gain = 250−200 = ₦50. %Gain = (50/200)×100% = 25%.

WAEC Mathematics 2012 Theory — Question 6

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