Question

A and B can complete a work in 24 days together, B and C can complete the same work in 36 days together and A and C can complete that work in 18 days together. In how many days C can complete the same work alone?
1. 60 days
2. 48 days
3. 72 days
4. 56 days
5. None of these.

Answer 1

Correct Answer - Option 2 : 48 days

Given:

Time to complete the whole work by A and B together = 24 days

Time to complete the whole work by B and C together = 36 days

Time to complete the whole work by A and C together = 18 days

Formula used:

Efficiency = Work Done/Time taken

Calculations:

Let the total work be LCM of 24, 36, 18 i.e. 72 units.

Let efficiency of A, B and C be A, B and C respectively.

Efficiency of A and B together,

⇒ A + B = 72/24 = 3 units/day      ----(i)

Efficiency of B and C together,

⇒ B + C = 72/36 = 2 units/day      ----(ii)

Efficiency of A and C together,

⇒ A + C = 72/18 = 4 units/day      ----(iii)

Adding equation (i), (ii) and (iii), we get,

(A + B) + (B + C) + (A + C) = 3 + 2 + 4

⇒ 2A + 2B + 2C = 9

⇒ A + B + C = 9/2 units/day

⇒ C = 9/2 - (A + B)

⇒ C = 9/2 - 3

⇒ C = 3/2

 Time taken by C to complete the whole work alone = 72/(3/2)

⇒ 48 days 

∴ C can complete the same work alone in 48 days.