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01 Oct 2020, 05:00
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C
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Difficulty:
75%
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Question Stats:
63% (02:42) correct
37%
(03:09)
wrong
based on 275
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The student population of a certain school increased a% from 1995 to 2005 and b% from 2005 to 2015. If the student population increased by 80% from 1995 to 2015 and the increase in the number of students in the second decade was three times the increase in the number of students in the first decade, what is the value of b?
A. 20
B. 26 2/3
C. 50
D. 60
E. 75
A. 20
B. 26 2/3
C. 50
D. 60
E. 75
01 Oct 2020, 05:20
Kudos
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Let initital number of students be 100
So, at the end of 2 decades the number of students = 180 (increased by 80%)
The increase was such that the increase in number of students in 2nd decade was thrice the increase in number of students in the first decade.
So, x + 3x = 80
so x = 20, 3x = 60
So, in the second decade the students increased by 60 heads.
So percentage of increase = 60/120 * 100% = 50% increase.
Ans C IMO
So, at the end of 2 decades the number of students = 180 (increased by 80%)
The increase was such that the increase in number of students in 2nd decade was thrice the increase in number of students in the first decade.
So, x + 3x = 80
so x = 20, 3x = 60
So, in the second decade the students increased by 60 heads.
So percentage of increase = 60/120 * 100% = 50% increase.
Ans C IMO
01 Oct 2020, 23:01
Kudos
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Let the number of students initially in 1995 = 100.
Therefore the total number of students in 2015 (80% increase) = \(100 * \frac{(100 + 80)}{100} = 180\)
The total increase = 180 - 100 = 80
Let x be the increase in the number of students in 1995 and 2005 (1st decade)
The increase in the number of students in the second decade = 3x (This has been stated)
Therefore the total increase x + 3x = 80
4x = 80 or x = 20
We have the following (1995) 100. This increased by 20 => (2005) 120. This increased by 3x = 60 => 2015 (180)
We have to calculate the % increase from 120 to 180
%\(Increase = \frac{Difference}{Smaller \space number} * 100 = \frac{180 - 120}{120} * 100 = 50\)%
Option C
Arun Kumar
Therefore the total number of students in 2015 (80% increase) = \(100 * \frac{(100 + 80)}{100} = 180\)
The total increase = 180 - 100 = 80
Let x be the increase in the number of students in 1995 and 2005 (1st decade)
The increase in the number of students in the second decade = 3x (This has been stated)
Therefore the total increase x + 3x = 80
4x = 80 or x = 20
We have the following (1995) 100. This increased by 20 => (2005) 120. This increased by 3x = 60 => 2015 (180)
We have to calculate the % increase from 120 to 180
%\(Increase = \frac{Difference}{Smaller \space number} * 100 = \frac{180 - 120}{120} * 100 = 50\)%
Option C
Arun Kumar
