Swati starts a business with Rs. 4,200 and after 5 months, Bani joins Swati as her partner. After a year, the profit is divided among Swati and Bani in the ratio 2:5. What is Bani's contribution?

Let's solve this step-by-step.

1. **Identify the time period each partner was involved in the business:**

   - Swati was involved for 12 months.
   - Bani joined after 5 months, so Bani was involved for \( 12 - 5 = 7 \) months.

2. **Let \( B \) be Bani's contribution.**

3. **Calculate the investment (capital) multiplied by the time for each partner:**

   - Swati: \( 4200 \times 12 = 50400 \)
   - Bani: \( B \times 7 \)

4. **According to the problem, the profit is divided in the ratio 2:5. Therefore, we set up the ratio of their investments multiplied by the time:**

   \[
   \frac{50400}{7B} = \frac{2}{5}
   \]

5. **Cross-multiplying to solve for \( B \):**

   \[
   50400 \times 5 = 2 \times 7B
   \]

   \[
   252000 = 14B
   \]

   \[
   B = \frac{252000}{14}
   \]

   \[
   B = 18000
   \]

So, Bani's contribution is **Rs. 18,000**.

Would you like a detailed explanation of any specific step or have any questions?

Here are some more questions you might find interesting:
1. How do you determine the ratio of investments in a partnership?
2. What is the formula for calculating simple interest?
3. How can you calculate compound interest?
4. What are the properties of different types of triangles?
5. How do you solve quadratic equations?

**Tip:** Always remember to keep track of the time period for each partner's investment when solving partnership problems.

Explore how to calculate Bani's contribution in a partnership problem where Swati starts a business with Rs. 4,200 and Bani joins after 5 months. The profit is divided in the ratio 2:5 after a year. Follow a step-by-step solution involving partnership concepts, ratios, and time calculations. Suitable for Grades 7-9.

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