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%
Related Questions
Know More about
Staff Selection Commission Sub Inspector ...
Application | Eligibility | Selection Process | Result | Cutoff | Admit Card | Preparation Tips
Get Updates Brochure
Your Staff Selection Commission Sub Inspector Exam brochure has been successfully mailed to your registered email id “”.
