A, B and C can complete a job in 5 days. B, C and D can complete the same job in 10 days. C, D and A can complete the same job in 15 days and D, A and B can complete the same job in 30 days. How long A, B, C and D together will take to finish the job?

7 days
\(7\frac{1}{2}\) days
8 days
\(8\frac{1}{2}\) days

Show answer & explanation

Answer: (B) \(7\frac{1}{2}\) days

Explanation

Adding the four group rates counts each person three times: 3(A + B + C + D) = 1/5 + 1/10 + 1/15 + 1/30 = 12/30. So A + B + C + D = 2/15 per day: 7½ days.