Anurag invested `33 1/3` % more than Ayush in a partnership and after one -year Ayush increased his share by 100 %. After two years they earned a profit of Rs. 15300 and Ayush got 10 % of total profit for managing business and rest profit is divided between both in ratio of their respective investment .Find the share of profit of Ayush ?

Options

A. A)8820 Rs
B. B)9260 Rs
C. C)9280 Rs
D. D)8860 Rs

Answer

To solve the problem step-by-step, we will break down the information provided and calculate Ayush's share of the profit.

### Step 1: Determine Initial Investments
Let Ayush's investment be \( x \).
Since Anurag invested \( 33 \frac{1}{3} \% \) more than Ayush, we can express Anurag's investment as:
\[ \text{Anurag's investment} = x + \frac{1}{3}x = \frac{4}{3}x \]

### Step 2: Calculate Investments Over Two Years
- For the first year:
- Anurag's investment = \( \frac{4}{3}x \)
- Ayush's investment = \( x \)

- For the second year, Ayush increased his investment by 100%, which means:
\[ \text{Ayush's new investment} = x + x = 2x \]

Thus, the investments over the two years are:
- Anurag: \( \frac{4}{3}x \) for 2 years
- Ayush: \( x \) for 1 year and \( 2x \) for 1 year

### Step 3: Calculate Total Investment Contribution
- Anurag's total contribution over 2 years:
\[ \text{Anurag's total} = \frac{4}{3}x \times 2 = \frac{8}{3}x \]

- Ayush's total contribution:
\[ \text{Ayush's total} = x \times 1 + 2x \times 1 = 3x \]

### Step 4: Calculate the Ratio of Investments
The ratio of their total investments is:
\[ \text{Ratio} = \frac{\text{Anurag's total}}{\text{Ayush's total}} = \frac{\frac{8}{3}x}{3x} = \frac{8}{9} \]

### Step 5: Calculate Profit Distribution
The total profit earned after 2 years is Rs. 15,300. Ayush receives 10% of this profit for managing the business:
\[ \text{Ayush's management share} = 10\% \text{ of } 15300 = \frac{10}{100} \times 15300 = 1530 \]

The remaining profit is:
\[ \text{Remaining profit} = 15300 - 1530 = 13770 \]

### Step 6: Divide Remaining Profit According to Investment Ratio
The remaining profit of Rs. 13,770 is divided in the ratio of 8:9 (Anurag:Ayush). The total parts = \( 8 + 9 = 17 \).

Ayush's share from the remaining profit:
\[ \text{Ayush's share from remaining profit} = \frac{9}{17} \times 13770 \]

Calculating this:
\[ \text{Ayush's share from remaining profit} = \frac{9 \times 13770}{17} = \frac{123930}{17} = 7290 \]

### Step 7: Calculate Total Share of Ayush
Now, we add Ayush's management share and his share from the remaining profit:
\[ \text{Total share of Ayush} = 1530 + 7290 = 8820 \]

### Final Answer
Thus, Ayush's share of the profit is:
\[ \boxed{8820} \]