Question

A is twice as efficient as B. If A and B together finish a job in 12 days, then number of days required for B to finish the job, is

• A. 18 days
• B. 24 days
• C. 30 days
• D. 36 days

Hint:

When efficiency ratio is given, assume unit efficiencies to simplify calculations.

Answer 1

The Correct Option is D

To solve the problem of determining the number of days B requires to finish the job alone, we follow these steps:

1. Let the work done by B in one day be \(1/x\) of the work.
2. According to the problem, A is twice as efficient as B. Hence, the work done by A in one day is \(2/x\) of the work.
3. When A and B work together, their combined work done in a day is the sum of their individual work per day. Therefore, A and B together complete \((2/x + 1/x) = 3/x\) of the work in one day.
4. It is given that A and B together can finish the job in 12 days. Therefore, the work done by them together in one day is \(1/12\) of the work.
5. Equating the total work done per day when working together to \(1/12\) of the work, we get: \(\frac{3}{x} = \frac{1}{12}\)
6. Solving for \(x\):
   • Cross-multiply to get \(3 \times 12 = x \times 1\), which simplifies to \(x = 36\).
7. The number of days B requires to finish the job alone is 36 days.

Thus, the correct answer is 36 days.