Varun can do a work in 28 days. In how many days can the work be completed by Sarvesh. if the efficiency of Sarvesh is 40% more than that of Varun?

Options

A. 18 days
B. 16 days
C. 20 days
D. 15 days

Answer

To solve the problem, we need to determine how many days Sarvesh can complete the work if his efficiency is 40% more than Varun's.

### Step-by-Step Solution:

1. **Determine Varun's Work Rate:**
- Varun can complete the work in 28 days.
- Therefore, Varun's work rate (efficiency) is \( \frac{1}{28} \) of the work per day.

2. **Calculate Sarvesh's Efficiency:**
- Sarvesh's efficiency is 40% more than Varun's.
- To find Sarvesh's efficiency, we calculate:
\[ \text{Sarvesh's efficiency} = \text{Varun's efficiency} + 0.4 \times \text{Varun's efficiency} \]
\[ = \frac{1}{28} + 0.4 \times \frac{1}{28} \]
\[ = \frac{1}{28} + \frac{0.4}{28} = \frac{1 + 0.4}{28} = \frac{1.4}{28} \]

3. **Simplify Sarvesh's Efficiency:**
- Now, simplify \( \frac{1.4}{28} \):
\[ = \frac{1.4 \div 1.4}{28 \div 1.4} = \frac{1}{20} \]
- Thus, Sarvesh's efficiency is \( \frac{1}{20} \) of the work per day.

4. **Calculate the Time Taken by Sarvesh:**
- If Sarvesh can do \( \frac{1}{20} \) of the work in one day, then the number of days (D) Sarvesh will take to complete the entire work is:
\[ D = \frac{1}{\text{Sarvesh's efficiency}} = \frac{1}{\frac{1}{20}} = 20 \text{ days} \]

### Final Answer:
Sarvesh can complete the work in **20 days**.