7) Raju started a business with Rs. 900. Kamal joined him after few months with an amount of 600. If the profits at the end of the year were divided in the ratio of 2:1, after how many months Kamal joined the business?

To solve this problem, we can use the concept of profit sharing based on the ratio of investments and the time for which the investments were made.

### Step 1: Understanding the problem
- Raju's investment: ₹900 for the entire year.
- Kamal's investment: ₹600, but only for a certain number of months (let's denote the number of months Kamal invested as \( x \)).
- The profit-sharing ratio is 2:1 in favor of Raju.

### Step 2: Setting up the equations
The profit ratio is directly proportional to the product of the investment and the time the investment was active. So:

- Raju’s share: \( 900 \times 12 \) (since he invested for the whole year)
- Kamal’s share: \( 600 \times x \) (where \( x \) is the number of months Kamal invested)

Given the ratio of their profits is \( \frac{2}{1} \):

\[
\frac{900 \times 12}{600 \times x} = \frac{2}{1}
\]

### Step 3: Simplifying the equation
Now, solve for \( x \):

\[
\frac{900 \times 12}{600 \times x} = 2
\]

\[
\frac{10800}{600 \times x} = 2
\]

\[
10800 = 1200 \times x
\]

\[
x = \frac{10800}{1200} = 9
\]

### Step 4: Conclusion
Kamal joined the business after **3 months** (since Kamal invested for \( 12 - 9 = 3 \) months of the year).

### Final Answer:
Kamal joined the business after **3 months**.

---

Would you like any further details on this solution? Here are some related questions you might find interesting:

1. How would the result change if Kamal had invested ₹900 instead?
2. What if the profit-sharing ratio was different, say 3:2? How would that affect the result?
3. How would the result change if Raju invested a different amount, say ₹1200?
4. What if Kamal had joined 2 months earlier? How would that affect the profit ratio?
5. How does the timing of the investment affect the overall profit-sharing in partnership problems?

**Tip:** In partnership problems, always remember that the share of profit is directly proportional to both the amount invested and the duration of the investment.

Raju started a business with Rs. 900. Kamal joined him after few months with an amount of 600. If the profits at the end of the year were divided in the ratio of 2:1, after how many months Kamal joined the business?

Learn how to solve a business partnership problem where the profits are divided in a 2:1 ratio. This problem involves calculating the time after which a partner joined the business using the concepts of profit sharing, ratios, and algebra. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation