WAEC 2010 · Paper 2 · Q6

(a)
In a class of 50 students, 30 offered History, 15 offered History and Geography while 3 did not offer any of the two subjects. (i) Represent the information on a Venn diagram. (ii) Find the number of students that offered: (A) History only; (B) Geography only.
Separate values with commas, e.g. 3, −2
(b)
A trader sold an article at a discount of $8\%$ for ₦828.00. If the article was initially marked to gain $25\%$ , find the: (i) cost price of the article; (ii) discount allowed.
Separate values with commas, e.g. 3, −2

Worked solution (try it first)

Draw two overlapping circles $H$ and $G$ inside a rectangle $U$ with $n(U) = 50$ .
Put 15 in the overlap and 3 outside both circles.

After an $8\%$ discount the price is $92\%$ of the marked price, so the marked price is $828 \times \frac{100}{92} =$ ₦900.00.

The marked price gives a $25\%$ gain, so it is $125\%$ of the cost price: cost price $= 900 \times \frac{100}{125} =$ ₦720.00.