Question

Two men and a woman are entrusted with a task. The second man needs three hours more to cope with the job than the first man and the woman would need working together. The first man, working alone, would need as much time as the second man and the woman working together. The first man, working alone, would spend eight hours less than the double period of time the second man would spend working alone. How much time would the two men and the woman need to complete the task if they all worked together?

• A. 2 hours
• B. 3 hours
• C. 4 hours
• D. 5 hours

Answer 1

The correct option is A 2 hours

In order to solve this question, if we look at the first statement, we could think of the following scenarios: If the time taken by the first man and the woman is 1 hour (100% work per hour), the time taken by the second man would be 4 hours (25% work per hour). In such a case, the total time taken by all three to complete the task would be $\frac{100}{125}=0.8$ hours. But this value is not there in the options. Hence, we reject this set of values.
If the time taken by the first man and the woman is 2 hours (50% work per hour), the time taken by the second man would be 5 hours (20% work per hour). In such a case, the total time taken by all three to complete the task would be $\frac{100}{70}=\frac{10}{7}$ hours. But this value is not there in the options. Hence, we reject this set of values.
If the time taken by the first man and the woman is 3 hours (33.33% work per hour), the time taken by the second man would be 6 hours (16.66% work per hour). In such a case, the total time taken by all three to complete the task would be $\frac{100}{50}=2$ hours. Since this value is there in the options we should try to see whether this set of values meets the other conditions in the question.
In this case, it is given that the first man working alone takes as much time as the second man and the woman. Since the work of all three is 50%, this means that the work of the first man is 25%. Consequently, the work of the woman is 8.33%.
Looking at the third condition given in the problem -the time taken by the first man to do the work alone (@ 25% per hour he would take 4 hours) should be 8 hours less than double the time taken by the second man. This condition can be seen to be fulfilled here because the second man would take 6 hours to complete his work (@ 16.66% per hour) and hence, double his time would be 12 hours which satisfies the difference of 8 hours.
Thus, the total time taken is 2 hours.