Question

If 8 men or 15 boys can do a work in 60 days. In how many days can 48 men and 10 boys complete the same work?

• A. 10
• B. 9
• C. 12
• D. 17
• E. 14

Answer 1

The Correct Option is B

Step 1: Understand the problem.
We are given that 8 men or 15 boys can do the work in 60 days. We need to find out how many days 48 men and 10 boys can complete the same work.

Step 2: Calculate the work done by one man and one boy.
Since 8 men can complete the work in 60 days, the total work in terms of man-days is:
Work = \( 8 \times 60 = 480 \) man-days.
Similarly, since 15 boys can complete the work in 60 days, the total work in terms of boy-days is:
Work = \( 15 \times 60 = 900 \) boy-days.

Step 3: Find the work done by one man and one boy per day.
The work done by one man in one day is \( \frac{1}{480} \) of the total work.
The work done by one boy in one day is \( \frac{1}{900} \) of the total work.

Step 4: Calculate the total work done by 48 men and 10 boys per day.
The total work done by 48 men and 10 boys per day is:
Work done by 48 men per day = \( 48 \times \frac{1}{480} = \frac{48}{480} = \frac{1}{10} \) of the total work per day.
Work done by 10 boys per day = \( 10 \times \frac{1}{900} = \frac{10}{900} = \frac{1}{90} \) of the total work per day.
Therefore, the total work done by 48 men and 10 boys per day is:
Total work per day = \( \frac{1}{10} + \frac{1}{90} = \frac{9}{90} + \frac{1}{90} = \frac{10}{90} = \frac{1}{9} \) of the total work per day.

Step 5: Calculate the number of days to complete the work.
Since they complete \( \frac{1}{9} \) of the work per day, the total time required to complete the work is:
Time = \( \frac{1}{\frac{1}{9}} = 9 \) days.

Step 6: Conclusion.
The work will be completed in 9 days.

Final Answer:
The correct option is (B): 9.