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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%


Team Careers360 24th Jan, 2024
Answer (1)
Team Careers360 25th Jan, 2024

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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