WAEC 2015 · Paper 2 · Q9

(a)
The first term of an Arithmetic Progression (A.P.) is $-8$ . If the ratio of the 7th term to the 9th term is $5 : 8$ , find the common difference of the A.P.
(b)
A trader bought 30 baskets of pawpaw and 100 baskets of mangoes for ₦2,450.00. She sold the pawpaw at a profit of $40\%$ and the mangoes at a profit of $30\%$ . If her profit on the entire transaction was ₦855.00, find the: (i) cost price of a basket of pawpaw; (ii) selling price of the 100 baskets of mangoes.
Separate values with commas, e.g. 3, −2

Worked solution (try it first)

Let a basket of pawpaw cost ₦ $p$ and a basket of mangoes cost ₦ $m$ .
Total cost: $30p + 100m = 2450$ (1).
Profit on pawpaw is $40\%$ of $30p$ and on mangoes $30\%$ of $100m$ : $0.4 \times 30p + 0.3 \times 100m = 855$ , which is $12p + 30m = 855$ (2).
Multiply (1) by 0.3: $9p + 30m = 735$ (3).
Take (3) from (2): $3p = 120$ , so $p = 40$ .