A and b can do a piece of work in 40 hours,b and c can do it 24 hours,and a and c can do the same work in 30 hours.in how many hours can a,b and c working together will finish the same piece of work?
Answers
Solution :
A and B can do a piece of work in 40 hours .
Therefore , work done by A and B in 1 hr is 1/40 th of the total work.
B and C can do a piece of work in 24 hours .
Therefore , work done by B and C in 1 hr is 1/24 th of the total work.
A and C can do a piece of work in 30 hours .
Therefore , work done by A and C in 1 hr is 1/30 th of the total work.
Now, these three equations are added
> Work done by A + Work done by B + Work done by B + Work done by C + Work done by C + Work done by A = 1/40 + 1/24 + 1/30
> 2(Work done by A + work done by B + work done by C ) = 1/40 + 1/24 + 1/30
> 2(Work done by A + work done by B + Work done by C ) = 1/10
> Work done by A + Work done by B + work done by C, all in 1 hr = 1/20.
Thus, the trio some will take 20 hours to finish the same work if they work together.
This is the required answer.
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