Correct Answer - Option 2 : 12.5 days

**Given :**

A is half as efficient as B, B is twice as efficient as C and B can do the work in 25 days.

**Concept used :**

work efficiency is inversely proportional to the time taken to complete the work.

**Calculations :**

Let the work efficiency of A, B and C be A, B and C .

A = B/2

⇒ A ∶ B = 1 ∶ 2

B = 2C

⇒ B ∶ C = 2 ∶ 1

So,

⇒ A ∶ B ∶ C = 1 ∶ 2 ∶ 1

Ratio of time for A, B and C = 1 ∶ 1/2 ∶ 1

⇒ 2 ∶ 1 ∶ 2

So, the time taken by A, B and C will be 50 days, 25 days and 50 days respectively.

⇒ (1/t) = (1/50) + (1/25) + (1/50) (where t is the time when all work together to finish the work)

⇒ 1/t = 4/50

⇒ t = 12.5 days

**∴ Option 2 will be the correct answer.**