Direct Proportion Calculation

When two quantities, $x$ and $y$, are in direct proportion, it means that as one quantity increases, the other quantity increases by the same factor. This relationship can be written as:

$y = kx$

where $k$ is the constant of proportionality.

Step 1: Find the Constant of Proportionality ($k$)

We are given that $y = 92.5$ when $x = 37$. We use these values to find $k$.

• Substitute the given values into the direct proportion formula:

  $92.5 = k \times 37$

• Solve for $k$:

  $k = \frac{92.5}{37}$

  $k = 2.5$

The constant of proportionality is $2.5$.

Step 2: Calculate the Value of $y$ when $x = 16$

Now, we use the constant $k = 2.5$ and the new value of $x = 16$ to find the corresponding value of $y$.

• Use the direct proportion formula again:

  $y = kx$

• Substitute $k = 2.5$ and $x = 16$:

  $y = 2.5 \times 16$

  $y = 40$

Therefore, when $x = 16$, the value of $y$ is $40$. This matches Option C.