Correct Answer - Option 3 : 14%
Given:
Decreasing 110 by x% gives the same result as increasing 50 by x%.
Calculations:
110 × (100 - x)/100 = 50 × (100 + x)/100
⇒ 11 × (100 - x) = 5 × (100 + x)
⇒ 1100 - 11x = 500 + 5x
⇒ 16x = 600
⇒ x = 600/16
⇒ x = 37.5
x% of 650 = 37.5% × 650
⇒ 243.75
(x - 10)% of 780 = (37.5 - 10)% × 780
⇒ 27.5% × 780
⇒ 214.50
Percentage difference = {(243.75 - 214.50)/214.50} × 100
⇒ (29.25/214.50) × 100
⇒ 13.63% ≈ 14%
∴ x% of 650 is 14% more than (x - 10)% of 780.