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) more than (x - 10)% of 780?

Solution(By Examveda Team)

$$\eqalign{ & 110 \times \frac{{\left( {100 - x} \right)}}{{100}} = 50 \times \frac{{\left( {100 + x} \right)}}{{100}} \cr & 11\left( {100 - x} \right) = 5\left( {100 + x} \right) \cr & 1100 - 11x = 500 + 5x \cr & 16x = 600 \cr & x = \frac{{800}}{{16}} = \frac{{75}}{2} = 37\frac{1}{2}\% \cr & {\text{Now,}} \cr & {\text{650}} \times \frac{{75}}{{200}} \to 780 \times \frac{{55}}{{200}} \cr & \frac{{25}}{2} \to 11 \cr & 25 \to 22 \cr & = \frac{3}{{22}} \times 100 = 14\% \cr} $$