Investment made by A and C is 40 % less and 60 % more than that of B respectively and ratio of period of investment of A,B and C are `3:2:1` . If average of their profit is Rs 21600 then find difference between A's and C's profit share (in Rs).

Options

A. A)2400
B. B)2000
C. C)1800
D. D)2600

Answer

To solve the problem, we will follow these steps:

### Step 1: Determine the investments of A, B, and C.
Let the investment of B be \( B = 100 \) units (this is a convenient choice to simplify calculations).

- A's investment is 40% less than B's:
\[ A = B - 0.4B = 100 - 40 = 60 \text{ units} \]

- C's investment is 60% more than B's:
\[ C = B + 0.6B = 100 + 60 = 160 \text{ units} \]

### Step 2: Write the ratio of investments.
The investments of A, B, and C can be summarized as:
\[ A : B : C = 60 : 100 : 160 \]
To simplify, we can divide each term by 20:
\[ A : B : C = 3 : 5 : 8 \]

### Step 3: Determine the ratio of time periods.
The ratio of the time periods of investment for A, B, and C is given as:
\[ A : B : C = 3 : 2 : 1 \]

### Step 4: Calculate the overall profit ratio.
The overall profit is determined by multiplying the investment by the time period for each person.

- For A:
\[ \text{Profit of A} = 3 \times 3 = 9 \text{ units} \]

- For B:
\[ \text{Profit of B} = 5 \times 2 = 10 \text{ units} \]

- For C:
\[ \text{Profit of C} = 8 \times 1 = 8 \text{ units} \]

Thus, the profit ratio is:
\[ A : B : C = 9 : 10 : 8 \]

### Step 5: Calculate the average profit.
The total profit units are:
\[ 9 + 10 + 8 = 27 \text{ units} \]
The average profit per person is:
\[ \text{Average profit} = \frac{27}{3} = 9 \text{ units} \]

### Step 6: Relate average profit to the given value.
We know the average profit is Rs 21,600, which corresponds to 9 units:
\[ 1 \text{ unit} = \frac{21600}{9} = 2400 \text{ Rs} \]

### Step 7: Calculate the profit shares.
Now, we can find the profit shares:
- A's profit:
\[ \text{Profit of A} = 9 \text{ units} \times 2400 = 21600 \text{ Rs} \]

- C's profit:
\[ \text{Profit of C} = 8 \text{ units} \times 2400 = 19200 \text{ Rs} \]

### Step 8: Find the difference between A's and C's profit share.
The difference between A's and C's profit share is:
\[ \text{Difference} = \text{Profit of A} - \text{Profit of C} = 21600 - 19200 = 2400 \text{ Rs} \]

### Final Answer:
The difference between A's and C's profit share is **Rs 2400**.

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