A. B and C invest Rs24,000/-, Rs132,00/-, and Rs48,000/-, for 4 months, 5 months and 6 months respectively. If total profit is Rs7,650/-, what is B's share ?

Options

A. Rs 2400
B. Rs 2250
C. Rs 2960
D. Rs 1122

Answer

To find B's share of the total profit, we first need to determine the investment contributions of A, B, and C in terms of "investment months," which is calculated by multiplying the amount invested by the number of months the investment is held.

### Step 1: Calculate the investment months for A, B, and C.

- For A:
\[ \text{Investment by A} = 24000 \text{ Rs} \times 4 \text{ months} = 96000 \text{ Rs-months} \]

- For B:
\[ \text{Investment by B} = 13200 \text{ Rs} \times 5 \text{ months} = 66000 \text{ Rs-months} \]

- For C:
\[ \text{Investment by C} = 48000 \text{ Rs} \times 6 \text{ months} = 288000 \text{ Rs-months} \]

### Step 2: Calculate the total investment months.

\[ \text{Total investment months} = 96000 + 66000 + 288000 = 450000 \text{ Rs-months} \]

### Step 3: Calculate the share of each partner in the total profit.

To find the share of profit for each partner, we first find the profit share ratio based on their investment months.

- A's share of profit:
\[ \text{A's share} = \frac{96000}{450000} \times 7650 \]

- B's share of profit:
\[ \text{B's share} = \frac{66000}{450000} \times 7650 \]

- C's share of profit:
\[ \text{C's share} = \frac{288000}{450000} \times 7650 \]

### Step 4: Calculate B's share specifically.

Calculating B's share:
\[ \text{B's share} = \frac{66000}{450000} \times 7650 \]

Calculating the fraction:
\[ \frac{66000}{450000} = \frac{11}{75} \]

Now, calculate B's share:
\[ \text{B's share} = \frac{11}{75} \times 7650 \]

Calculating the multiplication:
\[ \text{B's share} = \frac{11 \times 7650}{75} = \frac{84150}{75} = 1122 \]

### Final Answer:
B's share of the profit is Rs 1,122.

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