Question:
If \(x:y=4:5\), then \((5x+4y):(10x-2y)=\ ?\)
If \(x:y=4:5\), then \((5x+4y):(10x-2y)=\ ?\)
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When a ratio \(a:b\) is given, replace the quantities by \(ak\) and \(bk\). This simplifies ratio problems considerably.
Updated On: Jun 12, 2026
- \(1:2\)
- \(3:4\)
- \(4:3\)
- \(5:4\)
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The Correct Option is C
Solution and Explanation
Concept:
Whenever a ratio of two quantities is given, we may assume the quantities to be proportional to the terms of the ratio.
Given:
\[
x:y=4:5
\]
Let
\[
x=4k,\qquad y=5k
\]
where \(k\) is a non-zero constant.
Step 1: Substitute the values into the first expression. \[ 5x+4y \] \[ =5(4k)+4(5k) \] \[ =20k+20k \] \[ =40k \]
Step 2: Substitute the values into the second expression. \[ 10x-2y \] \[ =10(4k)-2(5k) \] \[ =40k-10k \] \[ =30k \]
Step 3: Form the required ratio. \[ (5x+4y):(10x-2y) = 40k:30k \] Cancelling the common factor \(10k\), \[ =4:3 \] Therefore, \[ \boxed{4:3} \]
Step 1: Substitute the values into the first expression. \[ 5x+4y \] \[ =5(4k)+4(5k) \] \[ =20k+20k \] \[ =40k \]
Step 2: Substitute the values into the second expression. \[ 10x-2y \] \[ =10(4k)-2(5k) \] \[ =40k-10k \] \[ =30k \]
Step 3: Form the required ratio. \[ (5x+4y):(10x-2y) = 40k:30k \] Cancelling the common factor \(10k\), \[ =4:3 \] Therefore, \[ \boxed{4:3} \]
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