A, B and C can do a piece of work in 10 days, 12 days and 15 days respectively.

Question:

A, B and C can do a piece of work in 10 days, 12 days and 15 days respectively. How long will they take to finish it if they work together?

Solution:

Time taken by A to complete the work $=10$ days

Time taken by B to complete the work $=12$ days

Time taken by C to complete the work $=15$ days

Work done per day by A $=\frac{1}{10}$

Work done per day by B $=\frac{1}{12}$

Work done per day by C $=\frac{1}{15}$

Total work done per day $=\frac{1}{10}+\frac{1}{12}+\frac{1}{15}=\frac{6+5+4}{60}=\frac{15}{60}=\frac{1}{4}$

A, B and C will take 4 days to complete the work if they work together.

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