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Exercise 7.3 The person A can doagetek in 5 days and the person B can do it in 8 days, in how many days will they do it together? The person cand they do it together 12 days while the person B can do it in 18 days. In how many days will it together? Two persons A and Borking together can mow a field in 6 hours. The person B alone can mow the field in 15 hours. In how many hours the person A can mow the heldi Roby and Zuby can do a piece of work separately in 30 and 20 hours respectively. In how many hours will they finish it working together? Twe persons A and B can do a piece of work in 12 hours. The person B alone can do it in 15 hours. In how many hours the person A alone can do it? Two persons A and B can make a house in 116 days and 118 days respectively, if they work alone. They work together for 30 days and then A falls sick. In how many days will B complete the remaining job? A contractor employed 20 men to build a tank and completed it in 10 days. After working together for 3 days, 5 men go home and do not return. How many days more will the remaining men take to complete the work? Three persons A, B and C working separately can do a work in 3, 7 and 5 days respectively. If they all work together and earn 4615 for the whole work, how much will each of them get? Two persons A and B together can do a piece of work in 10 days, persons B and C together can do it in 15 days, persons C and A together can do it in 12 days. How long will they take to finish the work, working altogether? How long would each take to do the same work? Three persons A, B and C working together can dig a pit in 15 days, whereas the person A alone can do it in 40 days and B alone can do it in 30 days. In what time, will the person C alone dig it? 2 Three persons A, B and C working together can plough a field in 105 days. The persons A and C together can do it in 16 days. If A alone can do it in 24 days, how long would A and B working together take to plough the field? 12. Two persons A and B together can build a wall in 12 days; persons B and C working together can do it in 10 days; persons C and A together can do it in 15 days. (i) In what time, working together, they will finish the work? (ii) In what time, working alone, each of them can do the same work? 14. A cistern can be filled by a tap in 4 hours and emptied by an outlet pipe in 16 hours. How 5 long will it take to fill the cistern if both the tap and the pipe are opened together. . Two taps A and B can fill a tank in 12 hours and 16 hours respectively and tap C, at the bottom, can empty it in 24 half three taps are opened together, when the tank filled completely is empty, in how many hou​

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yatharthgahane

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Step-by-step explanation:

Let's break down each exercise one by one:

Exercise 7.3:

1. **Person A can do a task in 5 days, and person B can do it in 8 days. How many days will they do it together?**

Let's find the rate at which each person works:

- Person A's rate = 1 task / 5 days = \( \frac{1}{5} \) task/day

- Person B's rate = 1 task / 8 days = \( \frac{1}{8} \) task/day

When they work together, their rates add up:

\( \text{Combined rate} = \frac{1}{5} + \frac{1}{8} = \frac{8 + 5}{40} = \frac{13}{40} \) task/day

To find the time taken for them to do the task together, we use the formula:

\( \text{Time} = \frac{\text{Total task}}{\text{Combined rate}} \)

\( \text{Time} = \frac{1}{\frac{13}{40}} = \frac{40}{13} \) days

Therefore, they will do the task together in \( \frac{40}{13} \) days.

2. **If person A can do the task alone in 12 days while person B can do it in 18 days, in how many days will they do it together?**

Following the same approach as above:

- Person A's rate = \( \frac{1}{12} \) task/day

- Person B's rate = \( \frac{1}{18} \) task/day

Combined rate:

\( \text{Combined rate} = \frac{1}{12} + \frac{1}{18} = \frac{3 + 2}{36} = \frac{5}{36} \) task/day

Time taken together:

\( \text{Time} = \frac{1}{\frac{5}{36}} = \frac{36}{5} \) days

Therefore, they will do the task together in \( \frac{36}{5} \) days.

3. **Two persons A and B working together can mow a field in 6 hours. The person B alone can mow the field in 15 hours. In how many hours can person A mow the field alone?**

Let's denote the time taken by person A to mow the field alone as \( x \) hours.

We use the formula: \( \text{Rate} = \frac{1}{\text{Time}} \)

- Combined rate when A and B work together = \( \frac{1}{6} \) field/hour

- Rate of person B working alone = \( \frac{1}{15} \) field/hour

From this, we can find the rate of person A working alone:

\( \text{Rate of A alone} + \text{Rate of B alone} = \text{Combined rate} \)

\( \text{Rate of A alone} = \text{Combined rate} - \text{Rate of B alone} \)

\( \text{Rate of A alone} = \frac{1}{6} - \frac{1}{15} = \frac{5 - 2}{30} = \frac{3}{30} = \frac{1}{10} \) field/hour

So, person A can mow the field alone in 10 hours.

4. **Roby and Zuby can do a piece of work separately in 30 and 20 hours respectively. In how many hours will they finish it working together?**

Let's denote the time taken by Roby to finish the work alone as \( R \) hours, and the time taken by Zuby to finish the work alone as \( Z \) hours.

Given:

\( R = 30 \) hours, \( Z = 20 \) hours

We use the formula: \( \text{Rate} = \frac{1}{\text{Time}} \)

- Rate of Roby = \( \frac{1}{30} \) work/hour

- Rate of Zuby = \( \frac{1}{20} \) work/hour

Their combined rate when working together:

\( \text{Combined rate} = \frac{1}{30} + \frac{1}{20} = \frac{2 + 3}{60} = \frac{5}{60} = \frac{1}{12} \) work/hour

So, they will finish the work together in 12 hours.

5. **Two persons A and B can do a piece of work in 12 hours. The person B alone can do it in 15 hours. In how many hours can person A alone do it?**

Let's denote the time taken by person A to finish the work alone as \( A \) hours, and the time taken by person B to finish the work alone as \( B \) hours.

Given:

\( A + B = 12 \) hours

\( B = 15 \) hours

We need to find \( A \).

Using the formula: \( \text{Time} = \frac{1}{\text{Rate}} \)

- Rate of A when working alone = \( \frac{1}{A} \) work/hour

- Rate of B when working alone = \( \frac{1}{15} \) work/hour

Their combined rate when working together is the same as the rate of work of A when working alone, since they can complete the work in the same time together as A alone.

So, \( A = 12 \) hours.

6. **Two persons A and B can make a house in 116 days and 118 days respectively, if they work alone. They work together for 30 days and then A falls sick. In how many days will B complete the remaining job?**

Let's find the rate at which A and B work together:

- Rate of A = \( \frac{1}{116} \) house/day

- Rate of B = \( \frac{1}{118} \) house/day

Their combined rate:

\( \text{Combined rate} = \frac{1}{116} + \frac{1}{118} \) house/day

They work together for 30 days, so the work done in 30 days is:

\( \text{Work done in 30 days} = \text{Combined rate} \times \text{Time} = \left( \frac{1}{116} + \frac{1}{118} \right) \times 30 \)

Subtracting this work from the total work gives us the remaining work that B needs to complete.

So, we find the work remaining as \( 1 - \left( \frac{1}{116} + \frac{1}{118} \right) \times 30 \).

We divide this remaining work by

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