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?

14%

110 × \(\frac{100 - x}{100}\) = 50 × \(\frac{100 + x}{100}\)

 11 × (100 - x) = 5 × (100 + x)

 1100 - 11x = 500 + 5x

 16x = 600

 x = \(\frac{600}{16}\)  = 37.5

Now ,

x% of 650 = 37.5% × 650 = \(\frac{137.5}{100}\) × 650

=  243.75

(x - 10)% of 780 = (37.5 - 10)% × 780

=  \(\frac{127.5}{100}\) × 780 =

= 214.50

Percentage difference = \(\frac{243.75 - 214.50}{214.50}\) × 100

 = \(\frac{29.25}{214.50}\) × 100 = 13.63%

= 14%    (approx)