Virat can complete a task a 20 days, whereas Anu can complete the same task in 15 days. How long will it take for Virat and Anu to complete the task if they worked together

Options

A. 12 `1/2` days
B. 5 days
C. `8 4/7` days
D. `17 1/2 days`

Answer

To find out how long it will take for Virat and Anu to complete the task if they work together, we can follow these steps:

### Step 1: Determine the work done by each person in one day.
- Virat can complete the task in 20 days. Therefore, his work in one day is:
\[ \text{Virat's 1 day work} = \frac{1}{20} \]

- Anu can complete the task in 15 days. Therefore, her work in one day is:
\[ \text{Anu's 1 day work} = \frac{1}{15} \]

### Step 2: Add the work done by both in one day.
- To find the total work done by both Virat and Anu in one day, we add their individual work rates:
\[ \text{Total work in one day} = \frac{1}{20} + \frac{1}{15} \]

### Step 3: Find a common denominator and simplify.
- The least common multiple (LCM) of 20 and 15 is 60. We can rewrite the fractions with the common denominator:
\[ \frac{1}{20} = \frac{3}{60} \quad \text{and} \quad \frac{1}{15} = \frac{4}{60} \]
- Therefore, adding these gives:
\[ \text{Total work in one day} = \frac{3}{60} + \frac{4}{60} = \frac{7}{60} \]

### Step 4: Calculate the total time taken to complete the task together.
- If they complete \(\frac{7}{60}\) of the task in one day, the total time taken to complete the entire task is the reciprocal of this amount:
\[ \text{Time taken} = \frac{1}{\frac{7}{60}} = \frac{60}{7} \text{ days} \]

### Step 5: Convert the time into a mixed number (if necessary).
- To express \(\frac{60}{7}\) in mixed number form:
\[ 60 \div 7 = 8 \quad \text{remainder} \quad 4 \]
- Thus, \(\frac{60}{7} = 8 \frac{4}{7}\) days.

### Final Answer:
Virat and Anu will take \(8 \frac{4}{7}\) days to complete the task if they work together.

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