R enter into a partnership in the ratio 2 : 3 : 5 . After 2 months, P increases his share 20% and Q by 10%. If the total profit at the end of one year is Rs 1,90,500, what amount will 'R' receive at the end of year as share in profit ?

Options

A. A) Rs. 90500
B. B) Rs. 87500
C. C) Rs. 88900
D. D) Rs. 90000

Answer

To solve the problem step by step, we will first determine the effective capital contribution of each partner over the year, taking into account the changes in their shares.

### Step 1: Determine the initial investment of P, Q, and R

The initial investment ratio of P, Q, and R is given as 2:3:5. Let's assume the initial investments are:
- P's investment = 2x
- Q's investment = 3x
- R's investment = 5x

### Step 2: Calculate the time each partner's investment is active

- P's investment (2x) is active for 12 months.
- Q's investment (3x) is active for 12 months.
- R's investment (5x) is active for 12 months.

After 2 months:
- P increases his investment by 20%, so his new investment becomes 2x * 1.2 = 2.4x. This new investment is active for the remaining 10 months.
- Q increases his investment by 10%, so his new investment becomes 3x * 1.1 = 3.3x. This new investment is also active for the remaining 10 months.
- R's investment remains 5x for the entire year (12 months).

### Step 3: Calculate the effective capital contribution for each partner

Now, we will calculate the effective capital contribution for each partner:

- **P's effective capital contribution:**
- For the first 2 months: 2x * 2 = 4x
- For the next 10 months: 2.4x * 10 = 24x
- Total for P = 4x + 24x = 28x

- **Q's effective capital contribution:**
- For the first 2 months: 3x * 2 = 6x
- For the next 10 months: 3.3x * 10 = 33x
- Total for Q = 6x + 33x = 39x

- **R's effective capital contribution:**
- For the entire year: 5x * 12 = 60x
- Total for R = 60x

### Step 4: Calculate the total effective capital contribution

Total effective capital contribution = P's contribution + Q's contribution + R's contribution
= 28x + 39x + 60x = 127x

### Step 5: Determine R's share of the profit

The total profit at the end of the year is Rs 1,90,500. Now we can find R's share of the profit:

R's share of the profit = (R's contribution / Total contribution) * Total profit
= (60x / 127x) * 1,90,500
= (60 / 127) * 1,90,500

### Step 6: Calculate R's profit share

Now, we will calculate R's share:

R's share = (60 / 127) * 1,90,500
= 60 * 1,90,500 / 127
= 1,14,300 / 127
≈ 60,000 (after calculation)

Thus, R will receive approximately Rs 60,000 as his share of the profit at the end of the year.

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