Aman and Raghav are two friends.
Aman started a business with an investment of Rs 7200, while Raghav puts 60% of his salary at 40% p.a simple interest for 6 months; Raghav takes the amount received after 6 months and joins Aman in the business. If Aman receives a profit of Rs. 2000 out of a total profit of Rs. 2900 at the end of 1 year, what was the original salary of Raghav?

To solve the problem, we need to determine Raghav's original salary based on the information given. Let’s break it down step by step:

### Step 1: Investment and Interest Calculation

Let Raghav’s monthly salary be \( S \). 

- Raghav invests 60% of his salary, i.e., \( 0.6S \), at a 40% per annum simple interest rate for 6 months. 
- The formula for simple interest is:

\[
I = \frac{P \times r \times t}{100}
\]

Where:
- \( P \) is the principal (in this case, \( 0.6S \)),
- \( r \) is the rate of interest (40% per annum),
- \( t \) is the time in years (6 months = 0.5 years).

Substitute the values:

\[
I = \frac{0.6S \times 40 \times 0.5}{100} = \frac{0.6S \times 20}{100} = 0.12S
\]

So, the interest earned is \( 0.12S \).

The total amount Raghav receives after 6 months is his principal plus interest:

\[
A = 0.6S + 0.12S = 0.72S
\]

### Step 2: Ratio of Investments

Now, Aman invests Rs. 7200, and Raghav invests the amount he receives after 6 months, which is \( 0.72S \). The total profit at the end of the year is Rs. 2900, out of which Aman receives Rs. 2000.

The profits are distributed in proportion to their investments. Therefore, the ratio of Aman's profit to Raghav's profit is the same as the ratio of their investments:

\[
\frac{\text{Aman's Profit}}{\text{Raghav's Profit}} = \frac{\text{Aman's Investment}}{\text{Raghav's Investment}}
\]

Substitute the given profit and the expressions for the investments:

\[
\frac{2000}{2900 - 2000} = \frac{7200}{0.72S}
\]

Simplify the equation:

\[
\frac{2000}{900} = \frac{7200}{0.72S}
\]

This simplifies to:

\[
\frac{20}{9} = \frac{7200}{0.72S}
\]

Cross-multiply:

\[
20 \times 0.72S = 9 \times 7200
\]

\[
14.4S = 64800
\]

Solve for \( S \):

\[
S = \frac{64800}{14.4} = 4500
\]

Thus, Raghav’s original salary is Rs. 4500.

### Final Answer:
Raghav’s original salary is Rs. 4500.

Would you like more details on any part of the solution?

Here are some follow-up questions to deepen understanding:

1. What would Raghav's salary be if he invested 70% instead of 60%?
2. How would the result change if the interest rate was 50% per annum?
3. What if Raghav joined the business after 9 months instead of 6 months?
4. How would Aman's profit change if he invested Rs. 8000 instead of Rs. 7200?
5. What would happen if Raghav received compound interest instead of simple interest?

**Tip:** Always double-check the proportion of profit sharing based on investments, as it plays a crucial role in determining outcomes in partnership problems.

Aman started a business with an investment of Rs 7200, while Raghav puts 60% of his salary at 40% p.a simple interest for 6 months; Raghav takes the amount received after 6 months and joins Aman in the business. If Aman receives a profit of Rs. 2000 out of a total profit of Rs. 2900 at the end of 1 year, what was the original salary of Raghav?

Solve a real-world business problem involving simple interest and profit sharing. Learn how to calculate Raghav's original salary, given that he invests 60% of his salary at 40% p.a simple interest for 6 months. Aman's and Raghav's profits are shared based on their investments. This problem includes core algebraic concepts and simple interest formula application, suitable for students in Grades 9-10.

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