Raman is 25% more efficient than Aman. If Aman can complete a piece of work in 25 days, then Raman can complete the same work in how many days?

Options

A. 12
B. 15
C. 16
D. 20

Answer

To solve the problem step by step, we will first determine the efficiency of Aman and then calculate Raman's efficiency based on the information given. Finally, we will find out how many days Raman would take to complete the same work.

### Step 1: Determine Aman's efficiency
Aman can complete the work in 25 days.
- Efficiency is defined as the amount of work done per day.
- If Aman completes the work in 25 days, his efficiency can be calculated as:

\[ \text{Efficiency of Aman} = \frac{1 \text{ work}}{25 \text{ days}} = \frac{1}{25} \text{ work/day} \]

### Step 2: Calculate Raman's efficiency
Raman is 25% more efficient than Aman.
- To find Raman's efficiency, we first need to calculate 25% of Aman's efficiency:

\[ 25\% \text{ of Aman's efficiency} = 0.25 \times \frac{1}{25} = \frac{1}{100} \text{ work/day} \]

- Now, we add this to Aman's efficiency to find Raman's efficiency:

\[ \text{Efficiency of Raman} = \text{Efficiency of Aman} + 25\% \text{ of Aman's efficiency} \]

\[ \text{Efficiency of Raman} = \frac{1}{25} + \frac{1}{100} \]

### Step 3: Find a common denominator and add the efficiencies
- The common denominator for 25 and 100 is 100. We convert Aman's efficiency:

\[ \frac{1}{25} = \frac{4}{100} \]

- Now, we can add the efficiencies:

\[ \text{Efficiency of Raman} = \frac{4}{100} + \frac{1}{100} = \frac{5}{100} = \frac{1}{20} \text{ work/day} \]

### Step 4: Calculate the number of days Raman takes to complete the work
- If Raman's efficiency is \(\frac{1}{20}\) work/day, then the number of days he takes to complete the work is the reciprocal of his efficiency:

\[ \text{Days taken by Raman} = \frac{1 \text{ work}}{\frac{1}{20} \text{ work/day}} = 20 \text{ days} \]

### Final Answer
Raman can complete the same work in **20 days**.