Kiran alone can do a piece of work in 15 days and Aman can do the same in 10 days. If they start working together, in how many days can the work be completed?

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Determine the work done by Kiran and Aman in one day.
- Kiran can complete the work in 15 days. Therefore, the work done by Kiran in one day is:
\[ \text{Work by Kiran in one day} = \frac{1}{15} \]

- Aman can complete the work in 10 days. Therefore, the work done by Aman in one day is:
\[ \text{Work by Aman in one day} = \frac{1}{10} \]

### Step 2: Find the combined work done by Kiran and Aman in one day.
- To find the total work done by both Kiran and Aman in one day, we add their individual work rates:
\[ \text{Combined work in one day} = \frac{1}{15} + \frac{1}{10} \]

### Step 3: Find a common denominator and add the fractions.
- The least common multiple (LCM) of 15 and 10 is 30. We convert the fractions:
\[ \frac{1}{15} = \frac{2}{30} \quad \text{and} \quad \frac{1}{10} = \frac{3}{30} \]
- Now, add the two fractions:
\[ \text{Combined work in one day} = \frac{2}{30} + \frac{3}{30} = \frac{5}{30} = \frac{1}{6} \]

### Step 4: Calculate the total time taken to complete the work together.
- If Kiran and Aman together can complete \(\frac{1}{6}\) of the work in one day, then the total time taken to complete the entire work is the reciprocal of their combined work:
\[ \text{Total time} = \frac{1}{\frac{1}{6}} = 6 \text{ days} \]

### Final Answer:
Kiran and Aman can complete the work together in **6 days**.

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