Understanding Profit Sharing Based on Investments

This problem involves calculating each partner's share of the annual profit based on their respective investments in a business. The profit is distributed proportionally to the amount each partner invested.

Calculating the Investment Ratio

First, we need to determine the ratio of investments made by Kiran, Vimal, and Naveen.

• Kiran's Investment: Rs. 1,35,000
• Vimal's Investment: Rs. 1,50,000
• Naveen's Investment: Rs. 1,65,000

The ratio of their investments is:

$$1,35,000 : 1,50,000 : 1,65,000$$

To simplify this ratio, we can divide all parts by their greatest common divisor. Let's start by dividing by 1,000:

$$135 : 150 : 165$$

Now, we can divide by 5:

$$ \frac{135}{5} : \frac{150}{5} : \frac{165}{5} = 27 : 30 : 33 $$

Next, we can divide by 3:

$$ \frac{27}{3} : \frac{30}{3} : \frac{33}{3} = 9 : 10 : 11 $$

So, the ratio of investments is 9 : 10 : 11.

Distributing the Total Profit

The total annual profit is Rs. 60,000. This profit needs to be divided among the partners according to the investment ratio (9 : 10 : 11).

First, calculate the sum of the ratio parts:

$$ \text{Sum of ratio parts} = 9 + 10 + 11 = 30 $$

Now, we can calculate the share for each partner:

Kiran's Share Calculation

Kiran's share is calculated using his part of the ratio:

$$ \text{Kiran's Share} = \left( \frac{\text{Kiran's Ratio Part}}{\text{Sum of Ratio Parts}} \right) \times \text{Total Profit} $$

$$ \text{Kiran's Share} = \left( \frac{9}{30} \right) \times 60,000 $$

$$ \text{Kiran's Share} = \frac{9}{30} \times 60,000 = 9 \times \frac{60,000}{30} = 9 \times 2,000 = 18,000 $$

Kiran's share is Rs. 18,000.

Vimal's Share Calculation

Vimal's share is calculated using his part of the ratio:

$$ \text{Vimal's Share} = \left( \frac{\text{Vimal's Ratio Part}}{\text{Sum of Ratio Parts}} \right) \times \text{Total Profit} $$

$$ \text{Vimal's Share} = \left( \frac{10}{30} \right) \times 60,000 $$

$$ \text{Vimal's Share} = \frac{10}{30} \times 60,000 = \frac{1}{3} \times 60,000 = 20,000 $$

Vimal's share is Rs. 20,000.

Naveen's Share Calculation

Naveen's share is calculated using his part of the ratio:

$$ \text{Naveen's Share} = \left( \frac{\text{Naveen's Ratio Part}}{\text{Sum of Ratio Parts}} \right) \times \text{Total Profit} $$

$$ \text{Naveen's Share} = \left( \frac{11}{30} \right) \times 60,000 $$

$$ \text{Naveen's Share} = \frac{11}{30} \times 60,000 = 11 \times \frac{60,000}{30} = 11 \times 2,000 = 22,000 $$

Naveen's share is Rs. 22,000.

Conclusion

The shares of Kiran, Vimal, and Naveen out of the Rs. 60,000 annual profit are Rs. 18,000, Rs. 20,000, and Rs. 22,000 respectively. This matches the second option provided.