Problem Solving

x is 40% less than y, z is 20% more than x, z is how much less than y?

Is it [spoiler]28%[/spoiler]

Plug in a value for Y (I like to use 100 whenever possible as it is easy to manipulate with %s)

If y = 100 then x = 60
Therefore, y = 72

(100 - 72)/100 * 100 = 28%

x=0.6 y and z=1.2x
=> z= 1.2 (0.6y) = 0.72y
Hence z is (1-0.72)*100 or 28% less than y

Great work from both responders, but let me offer a quick endorsement for the strategy proposed by kikor65! Whenever you are dealing with a percentage problem, plugging in 100 provides a quick and fool-proof way to handle the calculations. The algebraic method always WORKS, but the more complex the problem, the more time you'll save by plugging in. And time, ladies and gentlemen, is money! Or, points, which indirectly correlate to money

Cheers,

x = y - 40/100*y = 60y/100
z = x + 20/100*x = 120x/100 --(1)
substitute value of x in (1)
120*60/100*100 = 12*6/100 = 18/25 = .72 or 72% of y
calculate the answer by doing
y - z/y = (y - 72/100*y)/y = .28

kikor65 wrote:Plug in a value for Y (I like to use 100 whenever possible as it is easy to manipulate with %s)

If y = 100 then x = 60
Therefore, y = 72

(100 - 72)/100 * 100 = 28%

lol ...
yes i think this is the easist way ...
one should be careful about assuming the largest value 100 in this case Y.....(assming X=100 or z=100 adds up complications)

but in this reply,
u wrote y=72.....(i head rolled once...how much y=72 actaully z=72)...but later relaized that it was mistake....
any way minor but can sometime make a huge difference....during linear flow of mind...lol