A,B and c invested in a business in the ratio `6:8:9` .If B invested for a period whose numerical value is `112.5` % of B's investment but A and C invested -for -one year . If profit of B at the end of year is 16750 then what is the share of profit of C.

Options

A. A)20225
B. B)22125
C. C)25125
D. D)23125

Answer

To solve the problem step by step, we need to follow these calculations:

### Step 1: Understand the investment ratios
A, B, and C invested in the business in the ratio of 6:8:9. This means:
- A's investment = 6x
- B's investment = 8x
- C's investment = 9x

### Step 2: Determine the time of investment
- A and C invested for 1 year (12 months).
- B invested for a period that is 112.5% of his investment period.

To find the time B invested:
\[ \text{B's investment time} = 112.5\% \text{ of 8} = \frac{112.5}{100} \times 8 = 9 \text{ months} \]

### Step 3: Calculate the profit-sharing ratio
The profit-sharing ratio is determined by multiplying the investment amount by the time of investment for each partner.

- For A:
\[ \text{Profit of A} = 6 \times 12 = 72 \text{ units} \]

- For B:
\[ \text{Profit of B} = 8 \times 9 = 72 \text{ units} \]

- For C:
\[ \text{Profit of C} = 9 \times 12 = 108 \text{ units} \]

### Step 4: Combine the total profit units
Now we have the profit units:
- A = 72 units
- B = 72 units
- C = 108 units

Total profit units = 72 + 72 + 108 = 252 units.

### Step 5: Find the value of each unit
We know that B's profit at the end of the year is ₹16,750. Since B's profit corresponds to 72 units, we can find the value of each unit:
\[ \text{Value of each unit} = \frac{16750}{72} = 232.64 \text{ (approx)} \]

### Step 6: Calculate C's profit
Now we can find C's share of the profit:
\[ \text{C's profit} = 108 \text{ units} \times 232.64 = 25125.12 \text{ (approx)} \]

### Final Answer
C's share of the profit is approximately ₹25,125.

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