# A is half as efficient as B, B is twice as efficient as C. If B can do the work in 25 days, find in how many days the whole work will be completed if

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A is half as efficient as B, B is twice as efficient as C. If B can do the work in 25 days, find in how many days the whole work will be completed if they work together.

1. 10 days
2. 12.5 days
3. 15 days
4. 20 days

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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.