WAEC 2013 · Paper 2 · Q6

(a)
If $y^2 - x^2 = 5(y - x)^2$ , find $x : y$ .
Separate values with commas, e.g. 3, −2
(b)
In a partnership, Ajayi contributed ₦500,000.00 more than Kunle. The total profit made was $15\%$ of their total contribution. If Kunle received $\frac25$ of the total profit, which amounted to ₦84,000.00, how much was: (i) Ajayi's share of the profit? (ii) Kunle's contribution to the partnership?
Separate values with commas, e.g. 3, −2

Worked solution (try it first)

(a)

Expand the right-hand side: $5(y - x)^2 = 5y^2 - 10xy + 5x^2$ .
So $y^2 - x^2 = 5y^2 - 10xy + 5x^2$ .
Collect every term on one side: $4y^2 - 10xy + 6x^2 = 0$ .
Divide by 2: $2y^2 - 5xy + 3x^2 = 0$ .
Factorise: $(2y - 3x)(y - x) = 0$ .
Either $y = x$ , which gives $x : y = 1 : 1$ , or $2y = 3x$ , which gives $x : y = 2 : 3$ .

(b)(i)

$\frac25$ of the profit is ₦84,000, so the total profit is $84\,000 \times \frac52 = 210\,000$ , that is ₦210,000.
Ajayi gets the other $\frac35$ : $\frac35 \times 210\,000 = 126\,000$ .
Ajayi's share is ₦126,000.00.

(ii)

Let Kunle's contribution be ₦ $x$ .
Ajayi's is then ₦ $(x + 500\,000)$ , so together they put in ₦ $(2x + 500\,000)$ .
The profit is $15\%$ of the total: $\frac{15}{100}(2x + 500\,000) = 210\,000$ .
Multiply both sides by $\frac{100}{15}$ : $2x + 500\,000 = 1\,400\,000$ .
So $2x = 900\,000$ and $x = 450\,000$ .
Kunle contributed ₦450,000.00.

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