Question : If decreasing 110 by $x$% gives the same result as increasing 50 by $x$%, then $x$% of 650 is what percentage more than ($x$ + 20)% of 180? (correct to the nearest integer)
Option 1: 136%
Option 2: 90%
Option 3: 154%
Option 4: 80%
Correct Answer: 136%
Solution :
According to the question,
$110 \times \frac{100 - x}{100} = 50 \times \frac{100 + x}{100}$
⇒ $11 \times (100 - x) = 5 \times (100 + x)$
⇒ $1100 - 11x = 500 + 5x$
⇒ $16x = 600$
⇒ $x = \frac{600}{16}$
⇒ $x = 37.5$
Now, $x\% \times 650 = 37.5\% \times 650= 243.75$
Again, $(x +20)\% \times 180$
= $(37.5 + 20)\% \times 180$
= $\frac{57.5}{100} \times 180$
= $103.5$
Percentage difference = $\frac{(243.75 - 103.50)}{103.50} \times 100$
= $\frac{140.25}{103.50} \times 100$
= $135.51 \approx 136\%$
Hence, the correct answer is 136%.
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