Question

A and B can do a piece of work in 6 days; B and C can do the same work in 8 days; A and C can do the same work in 10 days. If A, B and C work together, how many days will it take them to complete the entire work?
1. \(2\frac{{18}}{{47}}\) days
2. \(5\frac{5}{{47}}\) days
3. \(3\frac{{32}}{{47}}\) days
4. None of the above

Answer 1

Correct Answer - Option 2 : \(5\frac{5}{{47}}\) days

Given:

A and B can do a piece of work in 6 days

B and C can do the same work in 8 days

A and C can do the same work in 10 days.

Calculation:

1 day work of A + B = 1/6

1 day work of B + C = 1/8

1 day work of C + A = 1/10

by adding,

1 day work of 2A + 2B + 2C = 1/6 + 1/8 + 1/10

⇒ 2(A + B + C) = (20 + 15 + 12)/120 = 47/120

⇒ 1 day work of A + B + C = 47/240

∴ The total time of A + B + C is 240/47 is \(5{5\over47}\)days.