Raju can make a certain amount of sweets in 12 hrs, while Sanju can eat same amount of sweets in 15 hrs. If they do their job alternatively after every 1 hour then in how much time the sweets will be prepared completely

Let's solve this problem step by step.

### 1. Rate of Work of Raju and Sanju:
- Raju can **make** a certain amount of sweets in 12 hours. So, in **1 hour**, he makes \(\frac{1}{12}\) of the total amount of sweets.
- Sanju can **eat** the same amount of sweets in 15 hours. So, in **1 hour**, he eats \(\frac{1}{15}\) of the total amount of sweets.

### 2. Work Done in 2 Hours:
Since they work alternately:
- In the first hour, Raju works and makes \(\frac{1}{12}\) of the sweets.
- In the second hour, Sanju works and eats \(\frac{1}{15}\) of the sweets.

After every 2 hours, the net amount of sweets prepared is:
\[
\frac{1}{12} - \frac{1}{15}
\]
To simplify this, find the common denominator of 12 and 15, which is 60:
\[
\frac{1}{12} = \frac{5}{60}, \quad \frac{1}{15} = \frac{4}{60}
\]
So, the net amount of sweets made in 2 hours is:
\[
\frac{5}{60} - \frac{4}{60} = \frac{1}{60}
\]
Therefore, in 2 hours, only \(\frac{1}{60}\) of the sweets are made.

### 3. Time Taken to Complete the Work:
The total amount of sweets is represented as 1 (the full job). Since \(\frac{1}{60}\) of the sweets is made every 2 hours, the total time required to complete the work is:
\[
1 \div \frac{1}{60} = 60 \times 2 = 120 \text{ hours}.
\]

Thus, it will take **120 hours** to prepare the sweets completely if they work alternately for 1 hour each.

Would you like more details, or do you have any questions?

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Here are 5 related questions to explore:
1. What would happen if Sanju eats sweets faster than Raju makes them?
2. How long would it take if they worked simultaneously?
3. How much of the sweets are left after 6 hours of alternating work?
4. If Raju took 15 hours to make the sweets, how would the time change?
5. What if Sanju ate sweets twice as fast? How would that affect the time?

**Tip:** In problems with alternating actions, finding net work over a cycle (e.g., 2 hours) helps simplify the solution.

Raju can make a certain amount of sweets in 12 hrs, while Sanju can eat the same amount of sweets in 15 hrs. If they do their job alternatively after every 1 hour then in how much time the sweets will be prepared completely?

Learn how to solve a work and time problem involving Raju and Sanju, where Raju makes and Sanju eats sweets alternately. The solution involves calculating their rates of work and finding the net work done over cycles. Suitable for Grades 6-8 students exploring work and time concepts in algebra.

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