WAEC 2018 · Paper 2 · Q8

(a)
Lamin bought a book for ₦300.00 and sold it to Bola at a profit of $x\%$ . Bola then sold the same book to James at a profit of $x\%$ . If James paid ₦ $\left(6x + \frac34\right)$ more for the book than what Lamin paid, find the value of $x$ .
(b)
Find the range of values of $x$ which satisfies the inequality $3x - 2 < 10 + x < 2 + 5x$ .
Show the answer
$2 < x < 6$

Worked solution (try it first)

Each sale multiplies the price by $1 + \frac{x}{100}$ .
Bola pays $300\left(1 + \frac{x}{100}\right) = 300 + 3x$ .
James pays $(300 + 3x)\left(1 + \frac{x}{100}\right) = 300 + 3x + 3x + \frac{3x^2}{100}$
$= 300 + 6x + \frac{3x^2}{100}$ .
James paid $6x + \frac34$ more than ₦300: $\frac{3x^2}{100} = \frac34$ , so $x^2 = 25$ and $x = 5$ (a percentage profit is positive).