WAEC 2008 · Paper 2 · Q7

(a)
When the marked price of an article is D600, the profit is $25\%$ . Calculate the: (i) cost price; (ii) actual profit if a $6\%$ cash discount is offered.
Separate values with commas, e.g. 3, −2
(b)
Isatu walks a distance of $1.5\text{ km}$ to school every day, her rate of walking always being constant. On a certain day, owing to ill health, she had to reduce her walking rate by $0.5\text{ km/h}$ and as a result she took 6 minutes longer than usual to reach the school. Find the normal average rate at which Isatu walks to school.

Worked solution (try it first)

Selling at the marked price gives $25\%$ profit, so D600 is $125\%$ of the cost price.
Cost price $= \frac{100}{125} \times 600 = 480$ , so D480.

With a $6\%$ discount she receives $94\%$ of the marked price: $\frac{94}{100} \times 600 = 564$ , so D564.
Actual profit = D564 − D480 = D84.

Let her normal rate be $v\text{ km/h}$ .
Her usual time is $\frac{1.5}{v}$ hours and her slow time is $\frac{1.5}{v - 0.5}$ hours.
Change 6 minutes to hours: $\frac{6}{60} = 0.1$ h.
So $\frac{1.5}{v - 0.5} - \frac{1.5}{v} = 0.1$ .
Multiply both sides by $v(v - 0.5)$ : $1.5v - 1.5(v - 0.5) = 0.1v(v - 0.5)$ , so $0.75 = 0.1v^2 - 0.05v$ .
Multiply both sides by 20: $15 = 2v^2 - v$ , so $2v^2 - v - 15 = 0$ .
Factorise: $(2v + 5)(v - 3) = 0$ , so $v = 3$ (a speed can't be negative).
Isatu normally walks at $3\text{ km/h}$ .