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Cyclist P increases his speed from 10 miles per hour to 25 miles per

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patnaiksonal
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Cyclist P increases his speed from 10 miles per hour to 25 miles per [#permalink] New post   Updated on: 19 Sep 2018, 20:18
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Cyclist P increases his speed from 10 miles per hour to 25 miles per hour in the last lap, while another Cyclist Q increases his speed from 8 miles per hour to 24 miles per hour in the last lap. By what percent is the percent increase in speed of Cyclist Q more than that of Cyclist P?

(A) 33.33
(B) 50
(C) 66.67
(D) 75
(E) 100
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A

Originally posted by patnaiksonal on 19 Sep 2018, 08:27.
Last edited by Bunuel on 19 Sep 2018, 20:18, edited 1 time in total.
Renamed the topic and edited the question.
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Re: Cyclist P increases his speed from 10 miles per hour to 25 miles per [#permalink] New post   19 Sep 2018, 08:36
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The % increase in 1st case is

(25-10)/10*100=150%

The % increase in 2nd case is

(24-8)/8*100=200%


Hence the % increase for the two cases is
(200-150)/150*100=33.33%
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Re: Cyclist P increases his speed from 10 miles per hour to 25 miles per [#permalink] New post   19 Sep 2018, 08:50
subhsngh0

why is it not 50%? (200% - 150%)
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Re: Cyclist P increases his speed from 10 miles per hour to 25 miles per [#permalink] New post   19 Sep 2018, 09:00
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patnaiksonal wrote:
Cyclist P increases his speed from 10 miles per hour to 25 miles per hour in the last lap, while
another Cyclist Q increases his speed from 8 miles per hour to 24 miles per hour in the last lap.
By what percent is the percent increase in speed of Cyclist Q more than that of Cyclist P?

(A) 33.33
(B) 50
(C) 66.67
(D) 75
(E) 100


OA: A

Cyclist P's Initial speed: 10 miles per hour
Cyclist P's Final speed: 25 miles per hour
Percentage increase in Cyclist P's speed : \(\frac{25-10}{10}*100=150\)%

Cyclist Q's Initial speed: 8 miles per hour
Cyclist P's Final speed: 24 miles per hour
Percentage increase in Cyclist P's speed : \(\frac{24-8}{8}*100=200\)%

Percentage difference between Cyclist Q and Cyclist P speed \(= (200-150)\)% \(= 50\)%

Required percentage \(= \frac{50%}{150%}*100 =33.3\)%
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Re: Cyclist P increases his speed from 10 miles per hour to 25 miles per [#permalink] New post   19 Sep 2018, 17:43
patnaiksonal wrote:

why is it not 50%? (200% - 150%)


Whenever you are calculating % increase you have divide the change(50 in this case) by original (150 in this case) then only you get the per cent change
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Re: Cyclist P increases his speed from 10 miles per hour to 25 miles per [#permalink] New post   25 Sep 2018, 10:19
Cyclist P increases speed by 150% and Cyclist Q increases speed by 200%

Q increases his speed by 50% more than the increase in P's speed or 50%/150%=33.33% (Option A is the correct ans)
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Re: Cyclist P increases his speed from 10 miles per hour to 25 miles per [#permalink] New post   30 Mar 2020, 09:23
patnaiksonal wrote:
Cyclist P increases his speed from 10 miles per hour to 25 miles per hour in the last lap, while another Cyclist Q increases his speed from 8 miles per hour to 24 miles per hour in the last lap. By what percent is the percent increase in speed of Cyclist Q more than that of Cyclist P?

(A) 33.33
(B) 50
(C) 66.67
(D) 75
(E) 100


Percent increase in speed of cyclist P = (25/10 - 1)*100% = 150%
Percent increase in speed of cyclist Q = (24/8 - 1)*100% = 200%

The percent is the percent increase in speed of Cyclist Q more than that of Cyclist P = 200%/150% - 1= 1/3*100% = 33.33%

IMO A
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Re: Cyclist P increases his speed from 10 miles per hour to 25 miles per [#permalink] New post   30 Jun 2023, 10:45
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Re: Cyclist P increases his speed from 10 miles per hour to 25 miles per [#permalink]
30 Jun 2023, 10:45
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