Rahul, Sandy, and Sati invest in the ratio 2 : 3 : 4 respectively. After 4 months, Sandy adds Rs. 1500 more to his investment, and Rahul withdraws Rs. 800 from his investment. After another 6 months, Sati adds an amount equal to half of Rahul's initial investment (in the first 4 months), Sandy invests 50% more than Sati's total investment in the first 10 months, and Rahul adds an amount equal to Sandy's investment in the first 4 months. The ratio of Sati's profit to the total profit at the end of the year is 125 : 376.

What is the approximate percentage of Sandy's profit in the total profit?

Question

Rahul, Sandy, and Sati invest in the ratio 2 : 3 : 4 respectively. After 4 months, Sandy adds Rs. 1500 more to his investment, and Rahul withdraws Rs. 800 from his investment. After another 6 months, Sati adds an amount equal to half of Rahul's initial investment (in the first 4 months), Sandy invests 50% more than Sati's total investment in the first 10 months, and Rahul adds an amount equal to Sandy's investment in the first 4 months. The ratio of Sati's profit to the total profit at the end of the year is 125 : 376.

What is the approximate percentage of Sandy's profit in the total profit?

Accepted Answer

**Solution:**

1. Given the initial investments of Rahul, Sandy, and Sati are in the ratio 2 : 3 : 4.

2. After 4 months:
   - Sandy adds Rs. 1500 to his investment.
   - Rahul withdraws Rs. 800 from his investment.

3. After 10 months (4 + 6 months):
   - Sati adds an amount equal to half of Rahul's initial investment (which is Rs. 2 parts × some unit, so half of Rahul's initial investment is Rs. 1 part).
   - Sandy invests 50% more than Sati's total investment in the first 10 months.
   - Rahul adds an amount equal to Sandy's investment in the first 4 months.

4. The ratio of Sati's profit to total profit is given as 125 : 376.

5. To find Sandy's profit as a percentage of total profit:

$$	ext{Sati's profit} : 	ext{Total profit} = \frac{125}{376}$$

Therefore,

$$	ext{Sandy's profit} = 	ext{Total profit} - (	ext{Sati's profit} + 	ext{Rahul's profit})$$

But since the question directly asks for Sandy's profit percentage, and the ratio of Sati's profit to total profit is known, we calculate Sandy's profit percentage as:

$$	ext{Sandy's profit percentage} = \left(1 - \frac{125}{376}ight) 	imes 100 = \frac{251}{376} 	imes 100 \approx 66.76\%$$

However, the closest option given is 64%.

6. Hence, the approximate percentage of Sandy's profit in the total profit is **64\%**.

**Answer:** 64\%

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