Anil, Dinesh and Deepak together can complete a work in 40 days. Anil and Dinesh together can complete the same work in 50 days. In how many days Deepak alone can complete the same work?

Options

A. 90 days
B. 200 days
C. 150 days
D. 75 days

Answer

To find out how many days Deepak alone can complete the work, we can use the information given in the problem and apply the formula for work done.

### Step-by-Step Solution:

1. **Understand the Work Rates:**
- Let the total work be represented as 1 unit of work.
- The work rate of Anil, Dinesh, and Deepak together (A + D + P) is:
\[ \text{Work rate of (A + D + P)} = \frac{1}{40} \text{ (since they complete the work in 40 days)} \]
- The work rate of Anil and Dinesh together (A + D) is:
\[ \text{Work rate of (A + D)} = \frac{1}{50} \text{ (since they complete the work in 50 days)} \]

2. **Calculate Deepak's Work Rate:**
- To find Deepak's work rate (P), we can use the relationship:
\[ \text{Work rate of (A + D + P)} - \text{Work rate of (A + D)} = \text{Work rate of P} \]
- Substituting the values:
\[ \frac{1}{40} - \frac{1}{50} = P \]

3. **Finding a Common Denominator:**
- The common denominator for 40 and 50 is 200. Thus, we convert the fractions:
\[ \frac{1}{40} = \frac{5}{200}, \quad \frac{1}{50} = \frac{4}{200} \]
- Now, substituting back:
\[ P = \frac{5}{200} - \frac{4}{200} = \frac{1}{200} \]

4. **Calculate Days for Deepak Alone:**
- Since Deepak's work rate is \(\frac{1}{200}\), it means he can complete the work in 200 days.
- Therefore, the number of days Deepak alone can complete the work is:
\[ \text{Days} = \frac{1}{P} = 200 \text{ days} \]

### Final Answer:
Deepak alone can complete the work in **200 days**.