A man,a woman and a boy can complete a piece of work in 20,30 and 60 days respectively.How many boys should join 2 men and 8 women to complete the work in 2 days?
To find out how many boys should join 2 men and 8 women to complete the work in 2 days, we need to determine the work efficiency of each individual and then calculate the total work that needs to be done.
Let's start by finding the work efficiency of each person:
- The man completes the work in 20 days, so his efficiency is 1/20 of the total work per day.
- The woman completes the work in 30 days, so her efficiency is 1/30 of the total work per day.
- The boy completes the work in 60 days, so his efficiency is 1/60 of the total work per day.
Now, let's calculate the combined efficiency of 2 men and 8 women working for 2 days:
- The combined efficiency of 2 men is (2/20) of the total work per day.
- The combined efficiency of 8 women is (8/30) of the total work per day.
To calculate the remaining work after 2 days, subtract the combined efficiency of 2 men and 8 women from the total work:
Remaining work = 1 - [(2/20) + (8/30)]
Next, let's calculate the number of boys needed to complete the remaining work in 2 days:
- The efficiency of each boy is 1/60 of the total work per day.
- Let's assume x boys are needed to complete the work in 2 days.
The combined efficiency of x boys is (x/60) of the total work per day.
Setting up the equation:
Remaining work = (x/60) * 2
Now, solve for x:
Remaining work = (x/60) * 2
Remaining work = x/30
Plug in the value of the remaining work:
Remaining work = 1 - [(2/20) + (8/30)]
Remaining work = 1 - (1/10 + 4/15)
Remaining work = 1 - (3/30 + 8/30)
Remaining work = 1 - (11/30)
Remaining work = 19/30
Therefore, we can set up the equation:
19/30 = x/30
Simplifying, we find:
x = 19
Hence, 19 boys should join 2 men and 8 women to complete the work in 2 days.