The correct answer is option (B):
9
Here's how to solve this problem, breaking down the steps for clarity:
First, let's establish the work rate of a single man and a single boy. We know the following:
* 8 men = 1 work in 60 days
* 15 boys = 1 work in 60 days
This means that the total amount of work is the same whether done by 8 men or 15 boys. Therefore we can relate the work rates of men and boys.
From the first statement, the amount of work done by one man in one day is 1/(8 * 60) of the total work, and similarly the work done by one boy in one day is 1/(15 * 60) of the total work.
We can express the work rate of a man in terms of the work rate of a boy. To do this, let's determine the relative work rates. Since the total work is the same, we can equate the total work done by men and boys in 60 days:
8 men * 60 days = 15 boys * 60 days
8 men = 15 boys (in terms of work rate)
1 man = (15/8) boys (in terms of work rate)
Now we can determine how much work 48 men and 10 boys can do. Let's convert all men to boys. Since 1 man is equivalent to (15/8) boys:
48 men = 48 * (15/8) boys = 90 boys
So, 48 men and 10 boys are equivalent to 90 boys + 10 boys = 100 boys.
We know 15 boys can complete the work in 60 days. Therefore 1 boy does 1/15th of the work in that time, and 100 boys will do 100/15ths or 20/3rds the work. To calculate the number of days required for 100 boys to complete the work, we can set up an inverse proportion:
If 15 boys take 60 days
then 100 boys will take x days
x = (15 boys * 60 days) / 100 boys = 9 days.
Therefore, 48 men and 10 boys can complete the work in 9 days.