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?
Answer & explanation
Correct answer: option 3
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)