Two friends P and Q started a business investing in the ratio of 5:6. R joined them after six months investing an amount equal to that of Q's. At the end of the year, 20% profit was earned which was equal to Rs. 98,000 What was the amount invested by R?

Options

A. Rs. 1,05,000
B. Rs. 1,75,000
C. Rs. 2,10,000
D. Data inadequate

Answer

To solve the problem step by step, we will follow the logical flow of the information provided in the question.

### Step 1: Understand the Investment Ratios
P and Q started a business investing in the ratio of 5:6. This means:
- Let the investment of P = 5x
- Let the investment of Q = 6x

### Step 2: Calculate the Duration of Investment
- P invested for 12 months (1 year).
- Q also invested for 12 months (1 year).
- R joined after 6 months and invested an amount equal to Q's, which is 6x, but only for 6 months.

### Step 3: Calculate the Effective Investment
To find the effective investment for profit sharing, we multiply the investment amount by the time period for which it was invested:
- Effective investment of P = 5x * 12 = 60x
- Effective investment of Q = 6x * 12 = 72x
- Effective investment of R = 6x * 6 = 36x

### Step 4: Calculate the Total Effective Investment
Now, we sum up the effective investments:
- Total effective investment = 60x + 72x + 36x = 168x

### Step 5: Determine the Total Profit
The total profit earned at the end of the year is given as Rs. 98,000, which is 20% of the total investment. Therefore, we can find the total investment:
- 20% of total investment = Rs. 98,000
- Total investment = Rs. 98,000 / 0.20 = Rs. 490,000

### Step 6: Find the Value of x
We know that the total effective investment is 168x, and we equate it to the total investment:
- 168x = 490,000
- x = 490,000 / 168
- x = 2916.67 (approximately)

### Step 7: Calculate the Amount Invested by R
R's investment is equal to 6x:
- Amount invested by R = 6x = 6 * 2916.67 = 17,500 (approximately)

### Final Answer
The amount invested by R is approximately **Rs. 17,500**.

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