Question : If decreasing 110 by $x\%$ gives the same result as increasing 50 by $x\%$, then $x\%$ of 650 is what percentage (correct to the nearest integer) is more than $(x-10)\%$ of 780?
Option 1: 12%
Option 2: 17%
Option 3: 14%
Option 4: 18%
Correct Answer: 14%
Solution : On decreasing 110 by $x\%$ as $110(1 - \frac{x}{100})$ and the increase of 50 by $x\%$ as $50(1 + \frac{x}{100})$. According to the question, $⇒110(1 - \frac{x}{100}) = 50(1 + \frac{x}{100})$ $⇒1100-11x=500+5x$ $⇒16x=600$ $⇒x=\frac{75}{2}$ $⇒x=37.5$% Next, we calculate $x\%$ of 650. So, 650 × $\frac{37.5}{100}$ = 243.75 Then,$(x-10)\%$ of 780. So, 780 × $\frac{27.5}{100}$ = 214.5 The required percentage = $\frac{243.75-214.5}{214.5}$ × 100 = 13.63% ≈ 14% Hence, the correct answer is 14%
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