BECE Mathematics 2018 Paper

Determine if the proportion is direct or indirectFor direct proportion, if one quantity is increased or decreased then the other quantity increases or decreases as well, respectively.But in indirect or inverse proportion, if one quantity increases then other quantity decreases and viceversa.In the question, you will realize that if more men work (workers increases) the work will be done earlier (days decreases), hence its an indirect or inverse proportionThus number of men is inversely proportional to the days for the jobYou can write the relation and solve for the constant $(k)$ using the known informationInversely proportional is 1 over what's its inversely proportional toRemove the proportionality sign by replacing with an equal to sign and a constant ( $k$ ) SimplifyMake $k$ the subject$k = \; \text{ men } \; x \; \text{ days } \;$Use the known values to solve for the constant ( $k$ )When 8 men, the days taken was 12$k = 8 \times 12$, for the sake of future cancellations, we can leave the answer this waySubstite the value of $k$ into the equation Since we are asked to find the days, you can make days the subject and subtitute the number of men into it to get the days.You can as well substite the men into the equation and solve for days. However you do it, you will arrive at the same answer Make days the subjectEvery number is being divided by 1 , hence $\text{men} = \frac{\text{men}}{1}$Rewrite the equationCross multiplymen $x$ days $= 1 \times 8 \times 12$Divide both sides by menmen cancels each other at the left side of the equation.Now calculate for the days for the 6 men 6 goes into itself, 1 and 12, 2 times days $= 8 \times 2 = 16$ days