BECE Mathematics 2015 Paper

Concept:The number of boys and the time taken are inversely proportional, because more boys means less time for the same work.Explanation:Let the number of boys be $w$ and the number of days be $d$.Since $w$ is inversely proportional to $d$, we write $w \propto \frac{1}{d}$.So, $w = \frac{k}{d}$, where $k$ is a constant.Using $w = 5$ boys and $d = 14$ days:$5 = \frac{k}{14}$Multiply both sides by 14:$k = 5 \times 14 = 70$So the relation is $w = \frac{70}{d}$.Now put $w = 7$ boys to find the required days:$7 = \frac{70}{d}$Multiply both sides by $d$:$7d = 70$Divide both sides by 7:$d = \frac{70}{7} = 10$ daysThus, 7 boys will take 10 days to cultivate the land.Answer:$10$ days (Option C)