A started with an investement of `₹ 28000`. Afterf 2 months , B joins with `₹ 20000` and after another two months C joins with `₹ 18000`. At the end of `10th` month from start of the business, if B withdraws `₹ 2000 and C withdraws `₹ 2000` what is the respective ratio in which profit shoubd be distributed among A,B and C at the end of the year ?

Options

A. `12:7:5`
B. `12:9:5`
C. `12:6:3`
D. `14:7:5`

Explanation

To solve the problem of profit distribution among A, B, and C, we need to calculate the effective capital contribution of each partner over the time they were invested in the business. We will calculate the capital contribution in terms of "months of investment" for each partner.

### Step 1: Calculate A's Contribution
A invests ₹28,000 for the entire year (12 months).

\[ \text{A's contribution} = 28000 \times 12 = 336000 \]

### Step 2: Calculate B's Contribution
B joins after 2 months and invests ₹20,000. Therefore, B's investment duration is 10 months.

\[ \text{B's contribution} = 20000 \times 10 = 200000 \]

### Step 3: Calculate C's Contribution
C joins after another 2 months (4 months from the start) and invests ₹18,000. Therefore, C's investment duration is 8 months.

\[ \text{C's contribution} = 18000 \times 8 = 144000 \]

### Step 4: Calculate Total Contributions
Now we can find the total contributions of A, B, and C.

\[ \text{Total contribution} = \text{A's contribution} + \text{B's contribution} + \text{C's contribution} \]

\[ \text{Total contribution} = 336000 + 200000 + 144000 = 680000 \]

### Step 5: Calculate the Ratio of Contributions
Now we can find the ratio of their contributions.

\[ \text{A : B : C} = 336000 : 200000 : 144000 \]

To simplify this ratio, we can divide each term by 16000 (the GCD of the three amounts):

\[ \text{A : B : C} = \frac{336000}{16000} : \frac{200000}{16000} : \frac{144000}{16000} \]

Calculating these gives:

\[ \text{A : B : C} = 21 : 12.5 : 9 \]

To express this in whole numbers, we can multiply through by 2:

\[ \text{A : B : C} = 42 : 25 : 18 \]

### Step 6: Final Ratio
Thus, the final ratio in which the profit should be distributed among A, B, and C is:

\[ \text{A : B : C} = 42 : 25 : 18 \]