Question

A B and C can do a piece of work in 12 15 and 20 days respectively how long will it take to do it working together?

Answer 1

5 days.

A, B and C can do the work in 12, 15 & 20 days respectively. They are essentially doing the same work, regardless of what the work is actually.The work will be equal for all of them. We don't know what unit of work is there to be done by them, only the days are given. For calculation, assume this units of work to be done be the LCM(Least common multiple) of all, so that we don't have to deal with fractions.

Now, LCM of 12, 15 & 20 is 60. So the total unit of work to be done is 60 units. Dividing 60 by respective days will give us efficiency of A,B & C. Which is

• A can do 5 unit of work in a day.
• B can do 4 unit of work in a day.
• C can do 3 unit of work in a day.​​​​​​

So they together does 12 units of work in a day (i.e. 4+3+5 =12)
​​​​​​
Total work is 60 units. So the total days required is 60/12 = 5 days.

Which means when A, B and C all together works, they need 5 days to complete the work.