A B C can do a work in 5, 10, 15 days respectively. they started working together but A and B left after 2 days. in how many days C can complete the remaining work

Let's break down the solution step by step.

### Step 1: Calculate the rate of work for A, B, and C.
- A can complete the work in 5 days. So, A’s rate of work = \( \frac{1}{5} \) of the work per day.
- B can complete the work in 10 days. So, B’s rate of work = \( \frac{1}{10} \) of the work per day.
- C can complete the work in 15 days. So, C’s rate of work = \( \frac{1}{15} \) of the work per day.

### Step 2: Determine how much work A, B, and C complete together in 2 days.
The combined rate of A, B, and C when working together:
\[
\text{Combined rate} = \frac{1}{5} + \frac{1}{10} + \frac{1}{15}
\]
We need to find a common denominator to sum these fractions:
\[
\text{Combined rate} = \frac{6}{30} + \frac{3}{30} + \frac{2}{30} = \frac{11}{30}
\]
So, together, they complete \( \frac{11}{30} \) of the work in 1 day.

In 2 days, they complete:
\[
2 \times \frac{11}{30} = \frac{22}{30} = \frac{11}{15}
\]
This means that in 2 days, A, B, and C together complete \( \frac{11}{15} \) of the total work.

### Step 3: Calculate the remaining work.
The total work is 1 unit, so the remaining work after 2 days is:
\[
1 - \frac{11}{15} = \frac{15}{15} - \frac{11}{15} = \frac{4}{15}
\]
Thus, \( \frac{4}{15} \) of the work is still remaining.

### Step 4: Calculate the time for C to complete the remaining work.
C’s rate of work is \( \frac{1}{15} \) of the work per day. To complete \( \frac{4}{15} \) of the work, the time required by C is:
\[
\text{Time} = \frac{4}{15} \div \frac{1}{15} = 4 \text{ days}
\]

### Final Answer:
C will take 4 more days to complete the remaining work after A and B leave.

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Would you like further details on any step?

### 5 Related Questions:
1. What happens if A, B, and C work together for more than 2 days?
2. How would the time change if B stayed for 1 more day before leaving?
3. Can you calculate the work done by C alone from the start?
4. What if A, B, and C had different work rates, such as 4, 8, and 12 days respectively?
5. How would the total time change if C left instead of A and B?

**Tip:** When combining rates of work, adding fractions with common denominators helps simplify the process.

A B C can do a work in 5, 10, 15 days respectively. They started working together but A and B left after 2 days. In how many days can C complete the remaining work?

Learn how to solve a work and time problem where A, B, and C can complete a task in 5, 10, and 15 days respectively. After A and B leave, find out how long it takes C to finish the remaining work. This solution covers key concepts in rates of work and fractional arithmetic. Suitable for students in Grades 6-8.

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