BECE Mathematics 2015 Paper

The more the workers, the lesser days it takes to complete the work Therefore number of workers is inversely proportional to days to complete work. Let $w=$ number of workers and $d=$ days $w \propto \frac{1}{d}$ Remove the proportionality by introducing equal to and a constant Let $k=$ constant $w = k \times \frac{1}{d}$$w = \frac{k}{d}$ Since we know the number of workers and days taken to complete the work, we can calculate for the value of $k$ $w = 5\;\text{boys}$$d = 14\;\text{days}$$5 = \frac{k}{14}$ Multiply both sides by 14 to get rid of the denominator.$5 \times 14 = k$ The general equation is therefore $w = \frac{5 \times 14}{d}$ Now we are given the number of workers to find number of days to complete the work. Number of workers $(w) = 7$$7 = \frac{5 \times 14}{d}$ Multiply both sides by $d$ to get rid of the denominator $7 \times d = 5 \times 14$ Solve for the value of $d$ by dividing both sides by 7 $d = \frac{5 \times 14}{7}$$d = 5 \times 2 = 10\;\text{days}$ Note: 7 divides itself once and 14, 2 times Days taken for the 7 boys to complete work is 10 days.