Study the information carefully and answer the questions that follow.
A, B and C started a business by investing Rs. 800, Rs. 1600 and Rs. 2000 respectively. In the second quarter, they invested amounts in the ratio 1 : 4 : 2. In the next quarter again, they invested amounts in the ratio 3 : 2 : 3. In the last quarter, the ratio of their investments were same as in the 2nd quarter. Also, in the last quarter, the respective amounts of A, B and C was double than the respective amounts invested in `2^(nd)` quarter. The total investment of C before `4^(th)` quarter was Rs 1400 more than that of A during the same duration. Also, ratio of B’s share in profit to total profit at the end of year was 66 : 153. Please note: All the investments were for one quarter only.
If A, B, C invested same amount in 1st quarter as given in the question in 1st quarter and the same amount as given in 2nd quarter in the question in 2nd, 3rd and 4th quarter, then what would be the profit of A at the end of year out of a total profit of Rs. 19,350?

Options

A. Rs. 2510
B. Rs. 3320
C. Rs. 2560
D. Rs. 3150

Explanation

To solve the problem step by step, we will break down the investments made by A, B, and C in each quarter and calculate their respective shares in the profit.

### Step 1: Initial Investments
- A invests Rs. 800
- B invests Rs. 1600
- C invests Rs. 2000

### Step 2: Second Quarter Investments
The investments are in the ratio 1:4:2. Let the common multiplier be \( x \).
- A's investment in the second quarter = \( 1x = x \)
- B's investment in the second quarter = \( 4x = 4x \)
- C's investment in the second quarter = \( 2x = 2x \)

### Step 3: Third Quarter Investments
The investments are in the ratio 3:2:3. Let the common multiplier be \( y \).
- A's investment in the third quarter = \( 3y \)
- B's investment in the third quarter = \( 2y \)
- C's investment in the third quarter = \( 3y \)

### Step 4: Fourth Quarter Investments
In the fourth quarter, the ratio of their investments is the same as in the second quarter, but the amounts are double.
- A's investment in the fourth quarter = \( 2 \times 1x = 2x \)
- B's investment in the fourth quarter = \( 2 \times 4x = 8x \)
- C's investment in the fourth quarter = \( 2 \times 2x = 4x \)

### Step 5: Total Investments Before the Fourth Quarter
- Total investment of A before the fourth quarter = \( 800 + x + 3y \)
- Total investment of B before the fourth quarter = \( 1600 + 4x + 2y \)
- Total investment of C before the fourth quarter = \( 2000 + 2x + 3y \)

### Step 6: Given Condition
The total investment of C before the fourth quarter is Rs. 1400 more than that of A:
\[ 2000 + 2x + 3y = 800 + x + 3y + 1400 \]
Simplifying this gives:
\[ 2000 + 2x + 3y = 2200 + x + 3y \]
\[ 2x - x = 2200 - 2000 \]
\[ x = 200 \]

### Step 7: Substitute \( x \) to Find Investments
Now substituting \( x = 200 \):
- A's investment in the second quarter = \( 200 \)
- B's investment in the second quarter = \( 800 \)
- C's investment in the second quarter = \( 400 \)

### Step 8: Calculate Total Investments
Now we can calculate the total investments:
- A's total investment = \( 800 + 200 + 3y + 2(200) \)
- B's total investment = \( 1600 + 800 + 2y + 8(200) \)
- C's total investment = \( 2000 + 400 + 3y + 4(200) \)

### Step 9: Calculate Profit Shares
The ratio of B's share in profit to total profit is given as \( 66:153 \). Thus, we can find the total profit share:
- Total profit = Rs. 19,350
- B's share in profit = \( \frac{66}{66 + 153} \times 19350 = \frac{66}{219} \times 19350 \)

### Step 10: Calculate A's Profit
To find A's profit, we need to find the ratio of A's investment to the total investment:
- Total investment = A's total investment + B's total investment + C's total investment
- A's profit = \( \frac{A's total investment}{Total investment} \times Total profit \)

### Final Calculation
After calculating the total investments and substituting the values, we can find A's share of the profit.