WAEC 2013 · Paper 2 · Q6

(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 $\dfrac{P^2 + q^2}{Pq}$ .
(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.

Worked solution (try it first)

(a)(i)

Their sum is three times their difference: $P + q = 3(P - q)$ .
Expand: $P + q = 3P - 3q$ .
So $4q = 2P$ and $P = 2q$ .

(ii)

Substitute $P = 2q$ : $\frac{P^2 + q^2}{Pq} = \frac{4q^2 + q^2}{2q \times q}$
$= \frac{5q^2}{2q^2}$
$= \frac52$
$= 2\frac12$ .

(b)

At 25 for ₦66, the 100 articles sold for $\frac{100}{25} \times 66 = ₦264$ .
That was a $32\%$ gain, so $264 = 1.32 \times$ cost price, and the cost price is $\frac{264}{1.32} = ₦200$ .
At 20 for ₦50 they would sell for $\frac{100}{20} \times 50 = ₦250$ .
Gain $= 250 - 200 = ₦50$ , which is $\frac{50}{200} \times 100\% = 25\%$ .
It is a gain of $25\%$ .

Report a problem with this question