If `(P)/(3) = (Q)/(4) = (R)/(5)`, then P : Q : R is :

Options

A. `3:5:6`
B. `3:4:6`
C. `3:4:5`
D. `2:3:5`

Answer

To solve the problem where \(\frac{P}{3} = \frac{Q}{4} = \frac{R}{5}\), we can follow these steps:

### Step 1: Set the common ratio
Let us denote the common ratio as \(k\). Therefore, we can express \(P\), \(Q\), and \(R\) in terms of \(k\):
\[ \frac{P}{3} = k \implies P = 3k \]
\[ \frac{Q}{4} = k \implies Q = 4k \]
\[ \frac{R}{5} = k \implies R = 5k \]

### Step 2: Write the ratio of \(P\), \(Q\), and \(R\)
Now we have:
\[ P = 3k, \quad Q = 4k, \quad R = 5k \]
We can express the ratio \(P : Q : R\) as:
\[ P : Q : R = 3k : 4k : 5k \]

### Step 3: Simplify the ratio
Since \(k\) is a common factor in all terms, we can cancel \(k\) from the ratio:
\[ P : Q : R = 3 : 4 : 5 \]

### Final Answer
Thus, the ratio \(P : Q : R\) is:
\[ \boxed{3 : 4 : 5} \]