Rama and Hari together can do a work in 15 days. Rama is twice as efficient as Hari. In how many days will Hari alone do the same work?

Options

A. 30 days
B. 25 days
C. 20 days
D. 45 days

Answer

To solve the problem step by step, we need to find out how many days Hari alone will take to complete the work.

### Step 1: Define the efficiencies of Rama and Hari.
Let the efficiency of Hari be \( H \). Since Rama is twice as efficient as Hari, we can denote Rama's efficiency as \( R = 2H \).

**Hint:** Efficiency is the amount of work done in a unit of time. If one person is twice as efficient as another, they can complete the same task in half the time.

### Step 2: Calculate the combined efficiency of Rama and Hari.
When Rama and Hari work together, their combined efficiency is:
\[ R + H = 2H + H = 3H \]

**Hint:** When two people work together, their efficiencies add up.

### Step 3: Determine the total work done in terms of efficiency.
If they can complete the work together in 15 days, then the total work can be expressed as:
\[ \text{Total Work} = \text{Combined Efficiency} \times \text{Time} = (3H) \times 15 = 45H \]

**Hint:** Total work can be calculated by multiplying the combined efficiency by the time taken.

### Step 4: Find the time taken by Hari alone to complete the work.
Since Hari's efficiency is \( H \), the time taken by Hari alone to complete the same work is:
\[ \text{Time taken by Hari} = \frac{\text{Total Work}}{\text{Efficiency of Hari}} = \frac{45H}{H} = 45 \text{ days} \]

**Hint:** To find the time taken by one person to complete a task, divide the total work by that person's efficiency.

### Conclusion:
Hari alone will take **45 days** to complete the work.

### Final Answer:
Hari will take **45 days** to complete the work alone.