If ratio of investment of A,B and C are in the ratio `3:5:8` and the time of investment of A,B and C are `100/3` % , 80 % and 25 % respectively of their investment , and profit of A is 4800 then what will be the profit of C.(in Rs)

Options

A. A)`25,600`
B. B)`15,600`
C. C)`24,800`
D. D)`22,500`

Answer

To solve the problem, we will follow these steps:

### Step 1: Understand the Ratios of Investment
The investments of A, B, and C are in the ratio of 3:5:8. We can denote their investments as:
- A's investment = 3x
- B's investment = 5x
- C's investment = 8x

### Step 2: Convert Time Percentages to Ratios
The time of investment for A, B, and C are given as:
- A: \( \frac{100}{3} \% = \frac{100}{3} \times \frac{1}{100} = \frac{1}{3} \) (in fraction)
- B: \( 80 \% = \frac{80}{100} = \frac{4}{5} \)
- C: \( 25 \% = \frac{25}{100} = \frac{1}{4} \)

Now, we can convert these fractions into a ratio based on the investments:
- A's time = \( \frac{1}{3} \) (1 unit of time)
- B's time = \( \frac{4}{5} \) (4 units of time)
- C's time = \( \frac{1}{4} \) (2 units of time)

### Step 3: Calculate Effective Investment Ratios
To find the effective investment ratios, we multiply the investment ratios by their respective time ratios:
- A's effective investment = \( 3x \times \frac{1}{3} = x \)
- B's effective investment = \( 5x \times \frac{4}{5} = 4x \)
- C's effective investment = \( 8x \times \frac{1}{4} = 2x \)

### Step 4: Find the Total Effective Investment
Now, we sum up the effective investments:
- Total = \( x + 4x + 2x = 7x \)

### Step 5: Calculate Profit Sharing Ratios
The profit sharing ratio is based on the effective investments:
- A's share = \( x \)
- B's share = \( 4x \)
- C's share = \( 2x \)

Thus, the profit sharing ratio is \( 1:4:2 \).

### Step 6: Calculate the Value of Each Unit of Profit
We know A's profit is Rs. 4800, which corresponds to 1 unit of profit. Therefore, the value of each unit of profit is:
- Value of 1 unit = \( \frac{4800}{1} = 4800 \)

### Step 7: Calculate C's Profit
C's profit corresponds to 2 units. Therefore, C's profit will be:
- C's profit = \( 2 \times 4800 = 9600 \)

### Final Answer
Thus, the profit of C is Rs. 9600.

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