If two times of A is equal to three times of B and also equal to four times of C, then `A : B : C` is:

Options

A. `2:3:4`
B. `3 : 4 : 2 `
C. `4 : 6 : 3 `
D. `6 : 4 : 3 `

Answer

To solve the problem, we start with the information given in the question:

1. We know that:
\[ 2A = 3B = 4C \]

2. Let's denote the common value of \(2A\), \(3B\), and \(4C\) as \(k\). Therefore, we can express \(A\), \(B\), and \(C\) in terms of \(k\):
\[ 2A = k \implies A = \frac{k}{2} \]
\[ 3B = k \implies B = \frac{k}{3} \]
\[ 4C = k \implies C = \frac{k}{4} \]

3. Now we have:
\[ A = \frac{k}{2}, \quad B = \frac{k}{3}, \quad C = \frac{k}{4} \]

4. To find the ratio \(A : B : C\), we can express them with a common denominator. The least common multiple (LCM) of the denominators \(2\), \(3\), and \(4\) is \(12\).

5. Now, we convert \(A\), \(B\), and \(C\) to have a denominator of \(12\):
\[ A = \frac{k}{2} = \frac{6k}{12} \]
\[ B = \frac{k}{3} = \frac{4k}{12} \]
\[ C = \frac{k}{4} = \frac{3k}{12} \]

6. Now we can write the ratio:
\[ A : B : C = 6k : 4k : 3k \]

7. We can simplify this ratio by dividing each term by \(k\):
\[ A : B : C = 6 : 4 : 3 \]

Thus, the final answer is:
\[ A : B : C = 6 : 4 : 3 \]