If increasing 60 by x% gives the same result as decreasing 100 by x%, then x% of 320 is what percent less than (x + 50)% of 160?
Answer & explanation
Correct answer: option 2
60 (100 + x)% = 100 (100 - x)%
3 (100 + x) = 5 (100 - x)
300 + 3x = 500 - 5x
8x = 200
x = 25
⇒ x% of 320 = 25% × 320 = 80
⇒ (x+50)% of 160 =(25+50)% × 160 = 75% of 160 = 120
Difference 120 - 80 = 40
Percent less = \(\frac{40}{120}\) × 100 = 33\(\frac{1}{3}\)%