Question:
If \( x \) is directly proportional to \( y \) and \( x = 10 \) when \( y = 2 \), what is \( x \) when \( y = 8 \)?
If \( x \) is directly proportional to \( y \) and \( x = 10 \) when \( y = 2 \), what is \( x \) when \( y = 8 \)?
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For direct proportionality, use the formula \( x = ky \), and solve for \( k \) using known values. Then use this value of \( k \) to find the unknown \( x \).
Updated On: Oct 6, 2025
- \( 30 \)
- \( 40 \)
- \( 50 \)
- \( 60 \)
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The Correct Option is B
Solution and Explanation
Step 1: Since \( x \) is directly proportional to \( y \), we can write the equation:
\[
x = ky,
\]
where \( k \) is the constant of proportionality.
Step 2: Use the given values \( x = 10 \) and \( y = 2 \) to find \( k \):
\[
10 = k \times 2
\Rightarrow
k = 5. \] Step 3: Now, when \( y = 8 \), substitute \( k = 5 \) into the equation: \[ x = 5 \times 8 = 40. \] Thus, \( x = 40 \).
\Rightarrow
k = 5. \] Step 3: Now, when \( y = 8 \), substitute \( k = 5 \) into the equation: \[ x = 5 \times 8 = 40. \] Thus, \( x = 40 \).
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