If 25% of x is 40 less than 30% of (x+60), then 35% of (x−40) is what percentage more than 120 ?

Options
a) $ 16 \frac 23$%
b) 20%
c) $ 12 \frac 13$%
d) $ 15 \frac 43$%

Solution

As per question
25% of x = $ \frac {x \times 25}{100} = \frac{x}{4}$
As per question: 25% of x is 40 less than 30% of (x+60),
30% of ( x+60) =$ ( x+60) \times \frac {30}{100} = \frac {3x +180}{10}$
$ \frac {x}{4} = \frac {3x + 180}{10} -40$
$ \frac {x}{4} = \frac {3x + 180 – 400}{10}$
10x = 4(3x – 220)
10x = 12x – 880
2x = 880
x= 440

35% of (x−40) is what percentage more than 120
35% of (x-40) is $ \frac{(440-40) \times 35}{100} = \frac {400 \times 35}{100}$ = 140
140 is more than 120 = 140 – 120 = 20
% more than $ \frac {20}{120} \times 100 = \frac {50}{3} = 16 \frac 23$%

Answer: $ 16 \frac 23$%