A and B can do a job in 5 days, B and C can do the same job in 6 days and C and A can do the same job in 7.5 days. A, B, and C together will complete the same job in how many days? 

A and B can do a job in 5 days, B and C can do the same job in 6 days and C and A can do the same job in 7.5 days. A, B, and C together will complete the same job in how many days?  Correct Answer 4

Given

A and B can do job in 5 days.

B and C can do job in 6 days.

C and A can do job in 7.5 days.

Formula used

Total work = Efficiency × Time taken

Calculation

Let total work be 30 units (LCM of 5, 6 and 7.5).

Now, efficiency of A + B = 30/5 = 6 unit/day      ---- (1)

And, efficiency of B + C = 30/6 = 5 units/day      ---- (2)

And, efficiency of A + C = 30/7.5 = 4 units/day      ---- (3)

Adding 1, 2 and 3, we get

2(A + B + C) = 15 units/day

⇒ A + B + C = 15/2 = 7.5 units/day

∴ Time taken by A, B and C to complete the work = 30/7.5 = 4 days