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?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e 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%
Hence x% of 650 is 14% more than (x - 10)% of 780