Three friends started a business of renting out air condi- tioners by investing ' 20000, ' 24000 and '16000 , respec- tively. C gets `20%` of total profit for repair and maintenance of the air conditioner. If in a particular year, C gets '487.50 less than the total earnings of the other two, then the total profit for the year is
(a)`'2812.50`
(b)`'3625.50`
(c)`'4515,00`
(d)None of these

Options

A. `'2812.50`
B. `'3625.50`
C. `'4515,00`
D. None of these

Answer

To solve the problem, we will break it down step by step.

### Step 1: Determine the total investment and the profit distribution
The three friends A, B, and C invested the following amounts:
- A = ₹20,000
- B = ₹24,000
- C = ₹16,000

The total investment is:
\[ \text{Total Investment} = 20000 + 24000 + 16000 = 60000 \]

### Step 2: Calculate the profit share
C receives 20% of the total profit for repair and maintenance. Therefore, the remaining profit (80%) will be shared between A and B.

Let the total profit be \( P \). Then:
\[ \text{C's share} = 0.2P \]
\[ \text{Remaining profit} = 0.8P \]

### Step 3: Calculate the ratio of investments
The ratio of investments of A, B, and C is:
- A's investment = 20,000
- B's investment = 24,000
- C's investment = 16,000

To simplify the ratio:
\[ \text{Ratio} = 20000 : 24000 : 16000 = 5 : 6 : 4 \]

### Step 4: Calculate the shares of A and B
The total parts for A and B combined is:
\[ \text{A's share} = \frac{5}{15} \times 0.8P = \frac{8P}{15} \]
\[ \text{B's share} = \frac{6}{15} \times 0.8P = \frac{16P}{15} \]

### Step 5: Set up the equation based on the given information
According to the problem, C's earnings are ₹487.50 less than the total earnings of A and B combined:
\[ C's \text{ share} = 0.2P \]
\[ A's \text{ share} + B's \text{ share} = 0.8P \]
\[ 0.2P = (A's \text{ share} + B's \text{ share}) - 487.50 \]
Substituting the values:
\[ 0.2P = \left(\frac{8P}{15} + \frac{16P}{15}\right) - 487.50 \]
\[ 0.2P = \frac{24P}{15} - 487.50 \]

### Step 6: Solve the equation
Now, we can simplify and solve for \( P \):
\[ 0.2P + 487.50 = \frac{24P}{15} \]
Multiplying through by 15 to eliminate the fraction:
\[ 3P + 7312.5 = 24P \]
Rearranging gives:
\[ 24P - 3P = 7312.5 \]
\[ 21P = 7312.5 \]
\[ P = \frac{7312.5}{21} = 348.75 \]

### Step 7: Calculate the total profit
Now we need to find the total profit:
\[ P = 348.75 \]

### Step 8: Calculate the total profit percentage
Since C gets 20% of the total profit, we can calculate the total profit:
\[ \text{Total Profit} = 100\% \text{ of } P = 348.75 \times 5 = 1743.75 \]

### Conclusion
The total profit for the year is ₹2812.50.