If \(x\) men working \(x\) hours a day for \(x\) days produce \(x\) units of work, how many units of work will \(y\) men working \(y\) hours a day for \(y\) days produce?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(\frac{y^{3}}{x^{2}}\)
Work done is proportional to men \(\times\) hours per day \(\times\) days. So the work done in one man-hour is the same in both cases.
First case: \(x\times x\times x=x^{3}\) man-hours produce \(x\) units
One man-hour produces \(\displaystyle \frac{x}{x^{3}}=\frac{1}{x^{2}}\) unit
Second case: \(y\times y\times y=y^{3}\) man-hours
Work produced \(\displaystyle =y^{3}\times\frac{1}{x^{2}}=\frac{y^{3}}{x^{2}}\) units