Amitabh, Brijesh and Kamlesh enter a partnership with shares in the ratio of 7/2: 4/3: 6/5 After 4 months, Amitabh increases his share by 50% . If the total profit at the end of the year be X 21600, what will be the share of Brijesh in the profit ?

Options

A. X 8000
B. X 12000
C. X 4000
D. X 7000

Answer

To solve the problem step by step, let's break it down:

### Step 1: Understand the Ratios
The shares of Amitabh, Brijesh, and Kamlesh are given in the ratio of \( \frac{7}{2} : \frac{4}{3} : \frac{6}{5} \).

### Step 2: Find a Common Denominator
To simplify the ratios, we need to find a common denominator for the fractions. The denominators are 2, 3, and 5. The least common multiple (LCM) of these numbers is 30.

### Step 3: Convert the Ratios
Now, we multiply each part of the ratio by 30 to eliminate the fractions:
- Amitabh's share: \( \frac{7}{2} \times 30 = 105 \)
- Brijesh's share: \( \frac{4}{3} \times 30 = 40 \)
- Kamlesh's share: \( \frac{6}{5} \times 30 = 36 \)

So, the new ratio of their shares is \( 105 : 40 : 36 \).

### Step 4: Calculate the Time Factor
Amitabh increases his share by 50% after 4 months. We need to calculate the effective capital contribution for each partner over the year (12 months):
- Amitabh contributes \( 105 \) for 4 months and \( 105 \times 1.5 = 157.5 \) for the remaining 8 months.
- Brijesh contributes \( 40 \) for 12 months.
- Kamlesh contributes \( 36 \) for 12 months.

### Step 5: Calculate Effective Contributions
Now, we calculate the effective contributions:
- Amitabh:
- For the first 4 months: \( 105 \times 4 = 420 \)
- For the next 8 months: \( 157.5 \times 8 = 1260 \)
- Total for Amitabh: \( 420 + 1260 = 1680 \)

- Brijesh:
- Total for Brijesh: \( 40 \times 12 = 480 \)

- Kamlesh:
- Total for Kamlesh: \( 36 \times 12 = 432 \)

### Step 6: Find the Total Contribution
Now, we sum up all the contributions:
- Total contribution = \( 1680 + 480 + 432 = 2592 \)

### Step 7: Find the Ratio of Contributions
Now we can find the ratio of their contributions:
- Amitabh: \( 1680 \)
- Brijesh: \( 480 \)
- Kamlesh: \( 432 \)

The ratio of their contributions is:
- \( 1680 : 480 : 432 \)

### Step 8: Simplify the Ratio
To simplify, we can divide each term by the greatest common divisor (GCD). The GCD of 1680, 480, and 432 is 48.
- Amitabh: \( \frac{1680}{48} = 35 \)
- Brijesh: \( \frac{480}{48} = 10 \)
- Kamlesh: \( \frac{432}{48} = 9 \)

So the simplified ratio is \( 35 : 10 : 9 \).

### Step 9: Calculate Brijesh's Share of Profit
The total profit is given as \( 21600 \).
- The total parts in the ratio = \( 35 + 10 + 9 = 54 \).
- Brijesh's share = \( \frac{10}{54} \times 21600 \).

### Step 10: Calculate the Final Amount
Calculating Brijesh's share:
\[ \text{Brijesh's share} = \frac{10}{54} \times 21600 = \frac{216000}{54} = 4000 \]

### Conclusion
Brijesh's share in the profit is **4000**.

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