If the investment of A, B and C are in the ratio of `1//2: 1//3: 1//4`. If the total profit is Rs 15600 for 1 year, then find the highest profit share?

Options

A. A)Rs 3600
B. B)Rs 2400
C. C)Rs 7200
D. D)Rs 4800

Answer

To solve the problem, we need to follow these steps:

### Step 1: Determine the investment ratios
The investments of A, B, and C are given in the ratio of \( \frac{1}{2} : \frac{1}{3} : \frac{1}{4} \).

### Step 2: Convert the ratios to a common base
To compare these fractions easily, we can find a common denominator. The denominators are 2, 3, and 4. The least common multiple (LCM) of these numbers is 12.

- For A: \( \frac{1}{2} = \frac{6}{12} \)
- For B: \( \frac{1}{3} = \frac{4}{12} \)
- For C: \( \frac{1}{4} = \frac{3}{12} \)

So, the investment ratios can be rewritten as:
- A : B : C = 6 : 4 : 3

### Step 3: Calculate the total parts in the ratio
Now, we add the parts of the ratio:
\[ 6 + 4 + 3 = 13 \]

### Step 4: Determine the value of each part
The total profit is Rs. 15,600. To find the value of one part, we divide the total profit by the total number of parts:
\[ \text{Value of one part} = \frac{15600}{13} = 1200 \]

### Step 5: Calculate the profit share for each person
Now, we can calculate the profit share for A, B, and C:
- Profit share of A = \( 6 \times 1200 = 7200 \)
- Profit share of B = \( 4 \times 1200 = 4800 \)
- Profit share of C = \( 3 \times 1200 = 3600 \)

### Step 6: Identify the highest profit share
From the calculated profit shares:
- A = 7200
- B = 4800
- C = 3600

The highest profit share is from A, which is Rs. 7200.

### Final Answer:
The highest profit share is Rs. 7200.

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