If decreasing 110 by x% gives the same result as increasing 50 by x%, then x% of 650 is what percentage more than (x+20)% of 180? (correct to the nearest integer)
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 136%.
Decreasing 110 by x% gives the same result as increasing 50 by x%.
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 + 20)% of 180 = (37.5 + 10)% × 180 = 57.5% × 180 = 103.50
Percentage difference = {(243.75 - 103.50)/103.50} × 100 = (140.25/103.50) × 100 = 135.5% ≈ 136%
x% of 650 is 136% more than (x + 20)% of 180.