If one third of A one fourth of B and one fifth of C are equal then A:B:C is

Options

A. 3 : 4 : 5
B. 4 : 3 : 5
C. 5 : 4 : 3
D. `1/3:1/4:1/5`

Answer

To solve the problem, we need to find the ratio of A, B, and C given that one third of A, one fourth of B, and one fifth of C are equal.

### Step-by-Step Solution:

1. **Set up the equation based on the given information:**
We know that:
\[ \frac{1}{3}A = \frac{1}{4}B = \frac{1}{5}C \]
Let's denote the common value of these expressions as \( k \). Therefore, we can write:
\[ \frac{1}{3}A = k \quad \Rightarrow \quad A = 3k \]
\[ \frac{1}{4}B = k \quad \Rightarrow \quad B = 4k \]
\[ \frac{1}{5}C = k \quad \Rightarrow \quad C = 5k \]

2. **Express A, B, and C in terms of k:**
From the above equations, we have:
- \( A = 3k \)
- \( B = 4k \)
- \( C = 5k \)

3. **Find the ratio A:B:C:**
Now we can write the ratio of A, B, and C:
\[ A:B:C = 3k : 4k : 5k \]
Since \( k \) is a common factor, we can simplify this to:
\[ A:B:C = 3 : 4 : 5 \]

### Final Answer:
Thus, the ratio A:B:C is \( 3:4:5 \).