m : n : 40 =5 : 20 : 10

To solve the proportion \( m : n : 40 = 5 : 20 : 10 \), we can set up the following equations based on the ratios given.

From the ratio \( 5 : 20 : 10 \), we can write:

• \( m = k \cdot 5 \)
• \( n = k \cdot 20 \)
• \( 40 = k \cdot 10 \)

To find \( k \), we can solve the equation involving 40: \[ 40 = k \cdot 10 \\ k = \frac{40}{10} = 4 \]

Now we can find \( m \) and \( n \):

• \( m = 5k = 5 \cdot 4 = 20 \)
• \( n = 20k = 20 \cdot 4 = 80 \)

Thus, the values of \( m \) and \( n \) are \( m = 20 \) and \( n = 80 \).

In summary: \[ m = 20, \; n = 80, \; 40 = 40 \]