If p:q=3:2 and q:r=6:5 then p:q:r is equal to

Options

A. 9:6:5
B. 9:6:10
C. 3:3:5
D. 3:6:5

Answer

To solve the problem of finding the ratio \( p:q:r \) given \( p:q = 3:2 \) and \( q:r = 6:5 \), we can follow these steps:

### Step 1: Express the ratios in terms of a common variable
From the given ratios, we can express \( p \) and \( q \) in terms of a common variable \( k \):
- Since \( p:q = 3:2 \), we can write:
\[ p = 3k \quad \text{and} \quad q = 2k \]

### Step 2: Express \( r \) in terms of \( q \)
Next, we will express \( r \) using the second ratio \( q:r = 6:5 \):
- From \( q:r = 6:5 \), we can write:
\[ q = 6m \quad \text{and} \quad r = 5m \]

### Step 3: Make \( q \) the same in both expressions
Now we need to make \( q \) the same in both expressions. We have \( q = 2k \) from the first ratio and \( q = 6m \) from the second ratio. To make them equal, we can set:
\[ 2k = 6m \]
From this equation, we can solve for \( k \) in terms of \( m \):
\[ k = 3m \]

### Step 4: Substitute \( k \) back into the expressions for \( p \) and \( r \)
Now we substitute \( k = 3m \) back into the expressions for \( p \) and \( r \):
- For \( p \):
\[ p = 3k = 3(3m) = 9m \]
- For \( r \):
\[ r = 5m \]

### Step 5: Write the final ratio \( p:q:r \)
Now we can express the ratio \( p:q:r \):
- We have:
\[ p = 9m, \quad q = 6m, \quad r = 5m \]
Thus, the ratio \( p:q:r \) can be written as:
\[ p:q:r = 9m:6m:5m \]
Since \( m \) is a common factor, we can simplify this to:
\[ p:q:r = 9:6:5 \]

### Final Answer
Therefore, the ratio \( p:q:r \) is equal to \( 9:6:5 \).

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