A, B and C enter into a partnership with shares in the ratio `7/2 :4/3:6/3` . After 4 months , A increase his share by 50 % . If the total profit at the end of the year was Rs 43200.Then , the B's share in the profit is :

Answer

To solve the problem step by step, we will follow the instructions provided in the video transcript and break down the calculations clearly.

### Step 1: Understand the Ratios
The shares of A, B, and C are given in the ratio \( \frac{7}{2} : \frac{4}{3} : \frac{6}{3} \).

### Step 2: Convert Ratios to a Common Format
To eliminate the fractions, we can find the least common multiple (LCM) of the denominators (2 and 3). The LCM is 6.

- For A: \( \frac{7}{2} \times 6 = 21 \)
- For B: \( \frac{4}{3} \times 6 = 8 \)
- For C: \( \frac{6}{3} \times 6 = 12 \)

Thus, the ratio of their shares becomes:
\[ A : B : C = 21 : 8 : 12 \]

### Step 3: Calculate the Effective Investment
A invests for 12 months, while B and C invest for the full year (12 months). However, A increases his share by 50% after 4 months.

- Initial investment of A for the first 4 months: \( 21 \times 4 = 84 \)
- After 4 months, A increases his share by 50%:
\[ \text{New share of A} = 21 + (0.5 \times 21) = 21 + 10.5 = 31.5 \]
- A's investment for the remaining 8 months: \( 31.5 \times 8 = 252 \)

### Step 4: Calculate Total Investments
Now, we calculate the total investments for A, B, and C:
- Total investment of A:
\[ 84 + 252 = 336 \]
- Total investment of B (for 12 months):
\[ 8 \times 12 = 96 \]
- Total investment of C (for 12 months):
\[ 12 \times 12 = 144 \]

### Step 5: Calculate Total Investment
Now we sum up the total investments:
\[ \text{Total Investment} = 336 + 96 + 144 = 576 \]

### Step 6: Calculate the Profit Share Ratios
The profit is distributed in the same ratio as their investments. The total profit is Rs 43,200.

### Step 7: Calculate the Value of Each Part
To find the value of one part of the profit:
\[ \text{Value of 1 part} = \frac{43200}{576} = 75 \]

### Step 8: Calculate B's Share in the Profit
B's share in the profit corresponds to his investment ratio of 8:
\[ \text{B's Share} = 8 \times 75 = 600 \]

### Final Answer
Thus, B's share in the profit is Rs 600.

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