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Three men A, B and C working together can do a work in 30 days. They start the work together and A works for 3 days and takes rest on the fourth day, B works for 5 days and takes rest on the next two days and C works for 7 days and takes rest on the next three days. In how many days will the work be completed ? (A, B, C work at the same rate)?
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Three men A, B and C working together can do a work in 30 days. They s...
Solution:

Given, A, B and C can do a work in 30 days
Let us assume that the total work to be done is 30 units of work (to make calculation easy)

Work done by A in 3 days = 3 x (1/30) = 1/10
Work done by B in 5 days = 5 x (1/30) = 1/6
Work done by C in 7 days = 7 x (1/30) = 7/30

Total work done in 4 days = 1/10 + 1/6 + 7/30 = 1/5
Work remaining after 4 days = 4/5

Total work done in 7 days = 1/10 + 1/6 + 7/30 + (2/3 x 1/6) + (3/4 x 7/30) = 2/3
Work remaining after 7 days = 1/3

Let x be the number of days required to complete the remaining work

Work done by A in x days = x x (1/30) = x/30
Work done by B in x days = x x (1/30) = x/30
Work done by C in x days = x x (1/30) = x/30

Total work done in x days = x/30 + x/30 + x/30 = x/10

Total work done in 4 + 7 + x days = 1 + 2/3 + x/10

1 + 2/3 + x/10 = 30/30 (since the total work is 30 units)

5/3 + x/10 = 1

x/10 = 1 - 5/3

x/10 = 1/3

x = 10/3 = 3.33

Therefore, the work will be completed in 4 + 7 + x = 14.33 days (approximately 14 days and 8 hours)

Answer: The work will be completed in approximately 14 days and 8 hours.
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Three men A, B and C working together can do a work in 30 days. They start the work together and A works for 3 days and takes rest on the fourth day, B works for 5 days and takes rest on the next two days and C works for 7 days and takes rest on the next three days. In how many days will the work be completed ? (A, B, C work at the same rate)?
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