If decreasing 120 by x% gives the same result as increasing 40 by x%, then x% of 210 is what percent less than (x+20)% of 180?
Answer & explanation
Correct answer: option 3
120 (100-x)% = 40 (100+x)%
3 (100-x) = 100+x
300 - 3x = 100+x
300 - 100 = x +3x
200 = 4x
50 = x
⇒ x% of 210 = 50% × 210 = 105
⇒ (x+20)% of 180 =(50+20)% × 180 = 70% of 180 = 126
Difference 126 - 105 = 21
Percent less = \(\frac{21}{126}\) × 100 = 16\(\frac{2}{3}\) %