Question : 15 men can complete a work in 25 days and 25 women can complete the same work in 40 days. If all the 15 men and 25 women work together, in how many days will the work get completed?
Option 1: $15 \frac{5}{13}$ days
Option 2: $10 \frac{5}{13}$ days
Option 3: $15 \frac{5}{12}$ days
Option 4: $15 \frac{4}{13}$ days
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Correct Answer: $15 \frac{5}{13}$ days
Solution : Total Work = LCM (925, 40) = 200 units. One day work of 15 men = $\frac{200}{25}$ = 8 units One day work of 25 women = $\frac{200}{40}$ = 5 units One day work of 15 men and 25 women working together = 8 + 5 = 13 units Time taken by 15 men and 25 women working together = $\frac{200}{13}$ = 15$\frac{5}{13}$ days. Hence the correct answer is 15$\frac{5}{13}$ days.
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