A, B and C invested different amounts in a business for 4 months, 6 months and 12 months respectively. B’s investment was 2 times A’s investment and C’s investment was 2.5 times A’s investment. If at the end of the year, they together received an amount of Rs 5819 as profit, what was B’s-share in the profit ?

Options

A. Rs 1,404
B. Rs 1,428
C. Rs 1,518
D. Rs 1,536

Answer

To solve the problem step by step, we will break down the information given and calculate B's share in the profit.

### Step 1: Define the Investments
Let A's investment be \( x \).
Then, according to the problem:
- B's investment = \( 2x \) (B's investment is 2 times A's)
- C's investment = \( 2.5x \) (C's investment is 2.5 times A's)

### Step 2: Define the Time Periods
The time periods for their investments are:
- A invests for 4 months
- B invests for 6 months
- C invests for 12 months

### Step 3: Calculate the Effective Investment
The effective investment can be calculated by multiplying the investment amount by the time period:
- A's effective investment = \( x \times 4 = 4x \)
- B's effective investment = \( 2x \times 6 = 12x \)
- C's effective investment = \( 2.5x \times 12 = 30x \)

### Step 4: Calculate the Total Effective Investment
Now, we sum up all the effective investments:
\[ \text{Total Effective Investment} = 4x + 12x + 30x = 46x \]

### Step 5: Determine the Profit Sharing Ratio
The profit sharing ratio is based on their effective investments:
- A's share = \( 4x \)
- B's share = \( 12x \)
- C's share = \( 30x \)

The total ratio of their shares is:
\[ \text{Total Ratio} = 4x : 12x : 30x = 4 : 12 : 30 \]

To simplify this ratio, we can divide each term by 2:
\[ = 2 : 6 : 15 \]

### Step 6: Calculate the Total Parts in the Ratio
Now, we find the total number of parts in the ratio:
\[ \text{Total Parts} = 2 + 6 + 15 = 23 \]

### Step 7: Calculate the Value of Each Part
The total profit is Rs 5819. To find the value of each part, we divide the total profit by the total parts:
\[ \text{Value of Each Part} = \frac{5819}{23} = 253 \]

### Step 8: Calculate B's Share
B's share corresponds to 6 parts of the total ratio:
\[ \text{B's Share} = 6 \times 253 = 1518 \]

### Conclusion
Thus, B's share in the profit is Rs 1518.