A, B and C enter into a partnership by investing their capitals in the ratio of 2/5:3/4:5/8 . After 4 months, A increased his capital by 50%, but B decreased his capital by 20%. What is the share of B in the total profit of ₹2,82,100 at the end of a years.

Options

A. a)₹97,500
B. b)₹1,01,400
C. c) ₹1,00,750
D. d) ₹83,200

Answer

To solve the problem step by step, we will follow these steps:

### Step 1: Determine the initial investment ratio
The initial investment ratios of A, B, and C are given as:
- A : B : C = 2/5 : 3/4 : 5/8

To simplify this ratio, we will find the least common multiple (LCM) of the denominators (5, 4, and 8). The LCM of 5, 4, and 8 is 40.

Now, we can convert each fraction to have a common denominator of 40:
- A's investment: \( \frac{2}{5} \times \frac{8}{8} = \frac{16}{40} \)
- B's investment: \( \frac{3}{4} \times \frac{10}{10} = \frac{30}{40} \)
- C's investment: \( \frac{5}{8} \times \frac{5}{5} = \frac{25}{40} \)

Thus, the simplified ratio is:
- A : B : C = 16 : 30 : 25

### Step 2: Calculate the effective capital after adjustments
A increases his capital by 50% after 4 months. Therefore, A's new capital becomes:
- A's new capital = \( 16 \times 1.5 = 24 \)

B decreases his capital by 20%. Therefore, B's new capital becomes:
- B's new capital = \( 30 \times 0.8 = 24 \)

C remains the same throughout the year:
- C's capital = 25

### Step 3: Calculate the time-weighted capital contributions
Now we need to calculate the effective capital contributions over the year (12 months):
- A's capital for the first 4 months = \( 16 \times 4 = 64 \)
- A's capital for the next 8 months = \( 24 \times 8 = 192 \)
- Total for A = \( 64 + 192 = 256 \)

- B's capital for the first 4 months = \( 30 \times 4 = 120 \)
- B's capital for the next 8 months = \( 24 \times 8 = 192 \)
- Total for B = \( 120 + 192 = 312 \)

- C's capital for the entire year (12 months) = \( 25 \times 12 = 300 \)

### Step 4: Calculate the total capital contributions
Now, we sum the total contributions:
- Total contributions = A + B + C = \( 256 + 312 + 300 = 868 \)

### Step 5: Calculate B's share of the profit
The total profit is ₹2,82,100. To find B's share, we first find B's ratio of the total contributions:
- B's share of the total = \( \frac{B's contribution}{Total contributions} = \frac{312}{868} \)

Now, we can calculate B's share of the profit:
- B's profit = \( \frac{312}{868} \times 282100 \)

Calculating this gives:
- B's profit = \( \frac{312 \times 282100}{868} \)
- B's profit = ₹ 1,01,400 (approximately)

### Final Answer:
B's share in the total profit is ₹1,01,400.

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