Ravi can complete a task in 6 days and Mohan can complete the same task in 9 days. In how many days can Ravi and Mohan together complete the same task?

Options

A. a)`3(3)/(5)` days
B. b)9 days
C. c)15 days
D. d)`3(2)/(5)` days

Answer

To solve the problem of how many days Ravi and Mohan can complete the task together, we can follow these steps:

### Step 1: Determine the work done by Ravi and Mohan in one day.

- Ravi can complete the task in 6 days. Therefore, the work done by Ravi in one day is:
\[ \text{Work done by Ravi in one day} = \frac{1}{6} \text{ of the task} \]

- Mohan can complete the task in 9 days. Therefore, the work done by Mohan in one day is:
\[ \text{Work done by Mohan in one day} = \frac{1}{9} \text{ of the task} \]

### Step 2: Calculate the total work done by both in one day.

- To find the total work done by both Ravi and Mohan in one day, we add their individual work rates:
\[ \text{Total work done in one day} = \frac{1}{6} + \frac{1}{9} \]

### Step 3: Find a common denominator and sum the fractions.

- The least common multiple (LCM) of 6 and 9 is 18. We can rewrite the fractions with a common denominator:
\[ \frac{1}{6} = \frac{3}{18} \quad \text{and} \quad \frac{1}{9} = \frac{2}{18} \]
- Now, add the fractions:
\[ \text{Total work done in one day} = \frac{3}{18} + \frac{2}{18} = \frac{5}{18} \]

### Step 4: Calculate the total time taken to complete the task together.

- If Ravi and Mohan together complete \(\frac{5}{18}\) of the task in one day, we need to find how many days it will take to complete the whole task (1 unit of work):
\[ \text{Days to complete the task} = \frac{1}{\frac{5}{18}} = \frac{18}{5} = 3.6 \text{ days} \]

### Conclusion:

Ravi and Mohan together can complete the task in **3.6 days**.

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