P,Q and R start a business P invests 3 times as much as Q invests and 2 0 invest -rd as much as R invests. Find 3 the ratio of capitals of P ,Q and R

Options

A. `3:2: 6`
B. `2:6:3`
C. `6:2:3`
D. `5:2:3`

Answer

To find the ratio of capitals of P, Q, and R, we can follow these steps:

### Step 1: Define the investment of P
Let the capital invested by P be \(6x\).

### Step 2: Determine the investment of Q
Since P invests 3 times as much as Q, we can express Q's investment as:
\[ \text{Investment of Q} = \frac{1}{3} \times \text{Investment of P} = \frac{1}{3} \times 6x = 2x \]

### Step 3: Determine the investment of R
According to the problem, P invests 2 times as much as R. Therefore, we can express R's investment as:
\[ \text{Investment of R} = \frac{1}{2} \times \text{Investment of P} = \frac{1}{2} \times 6x = 3x \]

### Step 4: Write the ratio of investments
Now we have the investments:
- Investment of P = \(6x\)
- Investment of Q = \(2x\)
- Investment of R = \(3x\)

The ratio of capitals of P, Q, and R can be expressed as:
\[ \text{Ratio of P : Q : R} = 6x : 2x : 3x \]

### Step 5: Simplify the ratio
To simplify the ratio, we can divide each term by \(x\):
\[ \text{Ratio of P : Q : R} = 6 : 2 : 3 \]

### Conclusion
Thus, the ratio of capitals of P, Q, and R is \(6 : 2 : 3\).

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