Teena and Rajeev started a partnership business with initial capitals of Rs. 1200 and Rs. 3200 respectively. After 7 months, Teena withdrew half of her initial investment, and at the same time, Rakesh joined the business with Rs. 4800. If the total profit at the end of the year is Rs. 1230, how much more is Rajeev's share of the profit compared to Teena's?

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**Solution:**

1. Calculate the effective capital contribution of each partner for the entire year considering the time period.

- Teena's capital for first 7 months = Rs. 1200
- After 7 months, she withdraws 50%, so remaining capital = Rs. 1200 × 50% = Rs. 600
- Teena's capital for last 5 months = Rs. 600

Teena's total capital contribution in terms of month-rupees:
$$1200 	imes 7 + 600 	imes 5 = 8400 + 3000 = 11400$$

2. Rajeev's capital remains Rs. 3200 for the whole 12 months:
$$3200 	imes 12 = 38400$$

3. Rakesh joins after 7 months with Rs. 4800 for the last 5 months:
$$4800 	imes 5 = 24000$$

4. Calculate the ratio of their investments:

Teena : Rajeev : Rakesh = 11400 : 38400 : 24000

Divide each by 600 to simplify:

$$\frac{11400}{600} : \frac{38400}{600} : \frac{24000}{600} = 19 : 64 : 40$$

5. Total profit = Rs. 1230

Sum of ratio parts = 19 + 64 + 40 = 123

6. Calculate Rajeev's and Teena's share:

- Rajeev's share = $\frac{64}{123} 	imes 1230 = 640$
- Teena's share = $\frac{19}{123} 	imes 1230 = 190$

7. Difference between Rajeev's and Teena's share:

$$640 - 190 = 450$$

**Answer:** Rs. 450

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