Percentage change

2014-12-17 1:33 am
If the population of city A is 25% more than the population of city B, then the population of city B is
A.20% less than the population of city A.
B.25% less than the population of city A.
C.75% less than the population of city A.
D.80% less than the population of city A.

I can't understand the answer using percentage change to solve it:
Let x be the population of city B.
Population of city A = x(1 + 25%) = 1.25x
(population of city A - population of city B)/ population of city A x 100%
= ((1.25x - x)/ 1.25x) x 100%
= 20%
∴The population of city B is 20% less than the population of city A.

回答 (1)

2014-12-17 3:34 am
✔ 最佳答案
When talking about ratio (i.e. % change), you need to take care of the numerator and denumerator. When A is 25% > B, A/B=1+25%, A=B(1+25%).
When the question changed to ask how many % B is < A, the numerator now changed to (A-B) and the denumerator changed to A. When you get the numerator and denumerator right, you'll get the right ratio (or %). Usually set a key variable will help simplify the calculation, the variable will always be eliminated as it appears inboth numerator and denumerator.

To discover the key variable, think about what profit/loss is relative to.
Let C be the cost of phone,
profit/loss = sold price - C
sold price=marked price x (1-discount %)
loss=cost - sold price; loss %=loss/cost
[C-5000x(1-30%)]/C=12.5%
C-3500=0.125C
C=3500/(1-0.125)=4000

profit=[5000x(1-discount%)-C]
By making discount % the subject,
discount %=1-(C+profit)/5000
=1-(4000+750)/5000
=5%
Answer is A.

2014-12-17 19:13:37 補充:
Don't know where you did wrong.
"a key variable": the 'x'. 'key': it is important and critical for ratio calculation; 'variable': the value can be kept unknown and eliminated (when both numerator and denumerator contain it) in some cases.


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