100 boys were employed to finish a work in 180 days. after 60 days it was found that only 1/4 of the work was done. how many more boys must be employed to finish the work in the stipulated time?
To solve this problem, we can use the concept of man-days.
First, let’s calculate the total man-days required to complete the work. If 100 boys are employed to finish the work in 180 days, then the total man-days required is obtained by multiplying the number of boys by the number of days:
Total man-days = 100 boys * 180 days = 18000 man-days
Next, let’s calculate the amount of work done in the first 60 days. Given that only 1/4 of the work was done in 60 days, we can calculate the amount of work done as:
Work done in 60 days = 1/4 * Total work
Work done in 60 days = 1/4 * 18000 man-days
Work done in 60 days = 4500 man-days
Now, let’s calculate the remaining work that needs to be completed:
Remaining work = Total work - Work done in 60 days
Remaining work = 18000 man-days - 4500 man-days
Remaining work = 13500 man-days
Since the work needs to be completed in the stipulated time of 180 days, and we already have 60 days worth of work done, we need to find the number of additional boys required to complete the remaining work in the remaining days (i.e., 120 days).
Let’s assume the number of additional boys required is x. The equation can be set up as follows:
(100 boys + x additional boys) * 120 days = 13500 man-days
Simplifying the equation, we have:
12000 boys + 120x = 13500
Subtracting 12000 from both sides, we get:
120x = 1500
Dividing both sides by 120, we find:
x = 12.5
Since we cannot have a fraction of a boy, we round up the value to the nearest whole number. Therefore, we need to employ 13 additional boys to finish the work in the stipulated time.