A, B and C start a business. A invests 3 times as much as B invests and B invests two-third of what C invests. Then, the ratio of capitals of A, B and Cis(

Options

A. (3:9:2)
B. (6:10:15)
C. (5:3:2)
D. (6:2:3)

Answer

To solve the problem step by step, let's denote the investments of A, B, and C as follows:

1. **Let the investment of C be \( x \)**.
2. **Since B invests two-thirds of what C invests**, we can express B's investment as:
\[ B = \frac{2}{3}x \]
3. **A invests three times as much as B**, so we can express A's investment as:
\[ A = 3B = 3 \left(\frac{2}{3}x\right) = 2x \]

Now we have the investments of A, B, and C in terms of \( x \):
- \( A = 2x \)
- \( B = \frac{2}{3}x \)
- \( C = x \)

4. **To find the ratio of their investments**, we express A, B, and C in a common form:
\[ A : B : C = 2x : \frac{2}{3}x : x \]

5. **To eliminate \( x \) from the ratio, we can multiply each term by 3 (the denominator of B's investment)**:
\[ A : B : C = 2x \cdot 3 : \frac{2}{3}x \cdot 3 : x \cdot 3 = 6x : 2x : 3x \]

6. **Now we can simplify the ratio**:
\[ A : B : C = 6 : 2 : 3 \]

Thus, the ratio of the capitals of A, B, and C is:
\[ \text{Ratio of A : B : C} = 6 : 2 : 3 \]