Ram, Dilip and Shekhar can complete a work in 20 days. If Ram and Dilip together can complete the same work in 30 days, then how long will Shekhar take to complete it ?

Options

A. 60 days
B. 62 days
C. 40 days
D. 56 days

Answer

To solve the problem step by step, let's denote the work done by Ram, Dilip, and Shekhar as follows:

1. **Understanding the Work Rates**:
- Let the total work be represented as 1 unit of work.
- Ram, Dilip, and Shekhar together can complete the work in 20 days. Therefore, their combined work rate is:
\[ \text{Work rate of Ram, Dilip, and Shekhar} = \frac{1}{20} \text{ (units of work per day)} \]

2. **Calculating the Work Rate of Ram and Dilip**:
- Ram and Dilip together can complete the work in 30 days. Thus, their combined work rate is:
\[ \text{Work rate of Ram and Dilip} = \frac{1}{30} \text{ (units of work per day)} \]

3. **Finding Shekhar's Work Rate**:
- We can find Shekhar's work rate by subtracting the work rate of Ram and Dilip from the combined work rate of Ram, Dilip, and Shekhar:
\[ \text{Work rate of Shekhar} = \text{Work rate of Ram, Dilip, and Shekhar} - \text{Work rate of Ram and Dilip} \]
\[ \text{Work rate of Shekhar} = \frac{1}{20} - \frac{1}{30} \]

4. **Finding a Common Denominator**:
- The least common multiple (LCM) of 20 and 30 is 60. We can rewrite the fractions:
\[ \frac{1}{20} = \frac{3}{60} \quad \text{and} \quad \frac{1}{30} = \frac{2}{60} \]
- Therefore:
\[ \text{Work rate of Shekhar} = \frac{3}{60} - \frac{2}{60} = \frac{1}{60} \]

5. **Calculating the Time Taken by Shekhar**:
- If Shekhar's work rate is \(\frac{1}{60}\), it means he can complete 1 unit of work in 60 days. Thus, the time taken by Shekhar to complete the work is:
\[ \text{Time taken by Shekhar} = 60 \text{ days} \]

So, Shekhar will take **60 days** to complete the work.