Question Number: 5
A, B and C can do a piece of work in 10 days, 15 days and 30 days respectively.
(a) In 1 day, how much work can be done by A and B? Answer: 1/6 part.
(b) In how many days they together can finish the work? Answer: 5 days.
(c) If after 3 days A left the work unfinished, in how many days the whole work will be finished? Answer: 7 days.

Let's solve the problem step by step.

### Given:
- A can complete the work in 10 days.
- B can complete the work in 15 days.
- C can complete the work in 30 days.

Let's calculate their daily work rates:

- **Work rate of A** = \( \frac{1}{10} \) work/day
- **Work rate of B** = \( \frac{1}{15} \) work/day
- **Work rate of C** = \( \frac{1}{30} \) work/day

### (a) In 1 day, how much work can be done by A and B?

The combined work rate of A and B:
\[
\text{Work rate of A and B} = \frac{1}{10} + \frac{1}{15}
\]

Finding the common denominator (which is 30):
\[
\frac{1}{10} = \frac{3}{30}, \quad \frac{1}{15} = \frac{2}{30}
\]
\[
\frac{1}{10} + \frac{1}{15} = \frac{3}{30} + \frac{2}{30} = \frac{5}{30} = \frac{1}{6}
\]

Therefore, A and B together can do \( \frac{1}{6} \) of the work in 1 day.

**Answer: \( \frac{1}{6} \) part**

### (b) In how many days can they together finish the work?

The combined work rate of A, B, and C:
\[
\frac{1}{10} + \frac{1}{15} + \frac{1}{30}
\]
Finding the common denominator (which is 30):
\[
\frac{1}{10} = \frac{3}{30}, \quad \frac{1}{15} = \frac{2}{30}, \quad \frac{1}{30} = \frac{1}{30}
\]
\[
\frac{1}{10} + \frac{1}{15} + \frac{1}{30} = \frac{3}{30} + \frac{2}{30} + \frac{1}{30} = \frac{6}{30} = \frac{1}{5}
\]

So, A, B, and C together can complete \( \frac{1}{5} \) of the work per day.

The total time to finish the work together is:
\[
\frac{1}{\frac{1}{5}} = 5 \text{ days}
\]

**Answer: 5 days**

### (c) If after 3 days A left the work unfinished, in how many days will the whole work be finished?

First, let's find out how much work is done in the first 3 days by A, B, and C together.

The work rate of A, B, and C together is \( \frac{1}{5} \) per day. Therefore, in 3 days, they will complete:
\[
3 \times \frac{1}{5} = \frac{3}{5}
\]

The remaining work is:
\[
1 - \frac{3}{5} = \frac{2}{5}
\]

Now, A leaves, so only B and C are working together. Their combined work rate:
\[
\frac{1}{15} + \frac{1}{30}
\]
Finding the common denominator (which is 30):
\[
\frac{1}{15} = \frac{2}{30}, \quad \frac{1}{30} = \frac{1}{30}
\]
\[
\frac{1}{15} + \frac{1}{30} = \frac{2}{30} + \frac{1}{30} = \frac{3}{30} = \frac{1}{10}
\]

B and C together can complete \( \frac{1}{10} \) of the work per day.

The time to complete the remaining \( \frac{2}{5} \) of the work is:
\[
\frac{\frac{2}{5}}{\frac{1}{10}} = 2 \times 2 = 4 \text{ days}
\]

Thus, the total time to finish the entire work is:
\[
3 + 4 = 7 \text{ days}
\]

**Answer: 7 days**

### Summary:
- (a) \( \frac{1}{6} \) part
- (b) 5 days
- (c) 7 days

Would you like any further details or clarifications?

### 5 Related Questions:
1. How much work can A and C complete together in 1 day?
2. If only B and C work together, in how many days will they complete the work?
3. What fraction of the work will be completed if A and B work together for 4 days?
4. How many days will A alone take to complete half the work?
5. If C works for 5 days alone, how much work is left to complete?

### Tip
Always break down combined work problems by calculating the individual work rates first and then summing them up!

A, B and C can do a piece of work in 10 days, 15 days and 30 days respectively.
(a) In 1 day, how much work can be done by A and B? Answer: 1/6 part.
(b) In how many days they together can finish the work? Answer: 5 days.
(c) If after 3 days A left the work unfinished, in how many days the whole work will be finished? Answer: 7 days.

Solve the work and time problem where A, B, and C complete a piece of work in 10, 15, and 30 days, respectively. Learn how to calculate how much work A and B can do together in 1 day, how long it takes all three to finish the work, and how many days it takes to finish if A leaves after 3 days.

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