If `(P)/(15)=(Q)/(21)=(R)/(7)` then find the ratio P:Q:R

Options

A. 7:21 : 93
B. 7:21:15
C. 93: 21:7
D. 15:21:7

Answer

To solve the problem, we start with the given equation:

\[ \frac{P}{15} = \frac{Q}{21} = \frac{R}{7} \]

Let's denote the common ratio as \( k \). This means we can express \( P \), \( Q \), and \( R \) in terms of \( k \):

1. From the equation \( \frac{P}{15} = k \), we can express \( P \) as:
\[ P = 15k \]

2. From the equation \( \frac{Q}{21} = k \), we can express \( Q \) as:
\[ Q = 21k \]

3. From the equation \( \frac{R}{7} = k \), we can express \( R \) as:
\[ R = 7k \]

Now we have \( P \), \( Q \), and \( R \) expressed in terms of \( k \):
- \( P = 15k \)
- \( Q = 21k \)
- \( R = 7k \)

Next, we need to find the ratio \( P : Q : R \):
\[ P : Q : R = 15k : 21k : 7k \]

Since \( k \) is a common factor, we can cancel it out:
\[ P : Q : R = 15 : 21 : 7 \]

Thus, the final answer for the ratio \( P : Q : R \) is:
\[ \boxed{15 : 21 : 7} \]