Question

45 men can complete a work in 16 days. After working for some days, 30 more men joined the work. As a result, work now finished in 6 days. How many days after the commencement of the work did the 30 persons join?

• A. 6
• B. 10
• C. 12
• D. 8

Hint:

When dealing with work problems, use the concept of man-days to relate work, workers, and time.

Answer 1

The Correct Option is A

Let the number of days the 45 men worked before the 30 men joined be \( x \). The total work required is: \[ \text{Total Work} = 45 \times 16 = 720 \, \text{man-days} \] After \( x \) days, 30 more men joined, making the total number of men \( 75 \). The remaining work is: \[ \text{Remaining Work} = 720 - 45x \] The remaining work is completed in 6 days by 75 men, so: \[ \text{Remaining Work} = 75 \times 6 = 450 \, \text{man-days} \] Now, equate the remaining work: \[ 720 - 45x = 450 \] \[ 45x = 270 \] \[ x = 6 \] Thus, 30 men joined after 12 days.