number first increases by 30% and then decreases by 20%. Find the percent increase or decrease on the
Answers
Answer:
1.5
Step-by-step explanation:
A number increases from 20 to 30 and then decreases from 30 to 20. Can you compare the percent of increase from 20 to 30 and that of the decrease from 30 to 20? Which is more, percent decrease or increase?
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Brett Schmidt
Answered 1 year ago
A number increases from 20 to 30 and then decreases from 30 to 20. Can you compare the percent of increase from 20 to 30 and that of the decrease from 30 to 20? Which is more, percent decrease or increase?
QUESTION:
Can you compare the percent of increase from 20 to 30 and that of decrease from 30 to 20? Which is more, percent decrease or increase?
MY ANSWER:
PERCENTAGE INCREASE:
(30-20)/20 = 10/20 = 1/2 = 0.5 = 50%. So an increase from 20 to 30 is an increase of 50% (of the initial value of 20).
PERCENTAGE DECREASE:
(20–30)/30 = (-10)/30 = -1/3 = -0.3333…. = -(33+1/3)% = -33.3333….%. So an decrease from 30 to 20 is a decrease of (33+1/3))% (of the initial value of 30).
So while the absolute change is the same (10) in both cases, the percentage increase is greater than the percentage decrease.
This is obviously a consequence of the fact that in the case of the increase, the change of 10 is a percentage of a lower number (20) than it is in the case of the decrease (30). In fact, the ratio of the percentage increase to the percentage decrease is equal to the ratio of the higher number to the lower number;
Percentage increase / percentage decrease
=5%/[(3+1/3)%]
= 5/(3+1/3)
= 5/(9/3+1/3)
= 5/[(9+1)/3] = 5/(10/3)
= 5×3/10
= 3/3
= 1.5 .
Higher number / lower number
= 30/20
= 3/2
= 1.5
Answer:
4% increase
Step-by-step explanation:
let the number be ⏩ 100
After 30% increament ⏩ 130
Than after 20% decrement ⏩104
hence 104-100=4
4% increament...