A, B and C enter into a partnership with capitals in the ratio `2/3 : 3/5 : 5/6`. After 8 month, A increases his share of capital by 25%.If at the end of the year, the total profit earned is ₹5,820, then the share of C in the profit is:

Options

A. ₹2,250
B. ₹2,350
C. ₹2,050
D. ₹2,450

Answer

To solve the problem step by step, we will follow the given information and perform calculations accordingly.

### Step 1: Determine the ratio of capitals
The capitals of A, B, and C are given in the ratio \( \frac{2}{3} : \frac{3}{5} : \frac{5}{6} \).

To simplify this ratio, we need to find a common denominator for the fractions. The least common multiple (LCM) of the denominators 3, 5, and 6 is 30.

Now, we convert each fraction to have a denominator of 30:
- A's capital: \( \frac{2}{3} = \frac{2 \times 10}{3 \times 10} = \frac{20}{30} \)
- B's capital: \( \frac{3}{5} = \frac{3 \times 6}{5 \times 6} = \frac{18}{30} \)
- C's capital: \( \frac{5}{6} = \frac{5 \times 5}{6 \times 5} = \frac{25}{30} \)

So, the ratio of capitals is \( 20 : 18 : 25 \).

### Step 2: Calculate the effective capital contribution of A, B, and C
A's capital is invested for 12 months, but for the last 4 months, he increases his capital by 25%.

Calculating A's capital for the first 8 months:
- A's capital for 8 months: \( 20 \times 8 = 160 \)

Calculating A's capital for the last 4 months after the increase:
- New capital of A after 25% increase:
\[ 20 \times \frac{125}{100} = 25 \]
- A's capital for 4 months: \( 25 \times 4 = 100 \)

Total contribution of A:
\[ 160 + 100 = 260 \]

B's capital is invested for the full 12 months:
- B's capital for 12 months: \( 18 \times 12 = 216 \)

C's capital is also invested for the full 12 months:
- C's capital for 12 months: \( 25 \times 12 = 300 \)

### Step 3: Calculate the total capital contributions
Now, we have:
- A's contribution: 260
- B's contribution: 216
- C's contribution: 300

### Step 4: Calculate the total profit share ratio
The total contributions are:
\[ 260 + 216 + 300 = 776 \]

Now, we can express the profit-sharing ratio:
- A's share: \( 260 \)
- B's share: \( 216 \)
- C's share: \( 300 \)

### Step 5: Calculate the share of C in the profit
The total profit is ₹5,820. To find C's share:
\[ \text{C's share} = \left( \frac{C's contribution}{Total contribution} \right) \times Total profit \]
\[ \text{C's share} = \left( \frac{300}{776} \right) \times 5820 \]

Calculating C's share:
\[ \text{C's share} = \frac{300 \times 5820}{776} \]
\[ \text{C's share} = \frac{1746000}{776} \approx 2245.16 \]

### Step 6: Rounding to the nearest whole number
Since profit shares are typically whole numbers, we round to the nearest integer:
C's share is approximately ₹2250.

### Final Answer
C's share in the profit is ₹2250.

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