WAEC 2021 · Paper 2 · Q6

(a)
In a class of 80 students, $\frac34$ study Biology and $\frac35$ study Physics. If each student studies at least one of the subjects: (i) draw a Venn diagram to represent this information; (ii) how many students study both subjects? (iii) find the fraction of the class that study Biology but not Physics.
Separate values with commas, e.g. 3, −2
(b)
Johnson and Jocatol Ltd. owned a business office with floor measuring $15\text{ m}$ by $8\text{ m}$ which was to be carpeted. The cost of carpeting was GH¢ 890.00 per square metre. If a total of GH¢ 216,120.00 was spent on painting and carpeting, how much was the cost of painting?

Worked solution (try it first)

Biology: $\frac34 \times 80 = 60$ students.
Physics: $\frac35 \times 80 = 48$ .
Draw two overlapping circles B and P in a rectangle of 80, with nobody outside (each studies at least one).
Let $x$ study both: B only $60 - x$ , P only $48 - x$ .

Biology but not Physics: $60 - 28 = 32$ students, which is $\frac{32}{80} = \frac25$ of the class.