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Percentage

by harsh.champ » Sun Feb 07, 2010 11:52 am
In a survey, it was found that the number of students in the college has increased by 20% over the previous year. The number of boys has increased by 10%, whereas the number of girls has increased by 35%. Find out the present percentage of girls in the college.

(A)40
(B)45
(C)55
(D)75
(E)60

The correct answer is B.
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by shashank.ism » Sun Feb 07, 2010 11:54 am
harsh.champ wrote:In a survey, it was found that the number of students in the college has increased by 20% over the previous year. The number of boys has increased by 10%, whereas the number of girls has increased by 35%. Find out the present percentage of girls in the college.

(A)40
(B)45
(C)55
(D)75
(E)60

The correct answer is B.
Let X be the total no. of students, B be the no. of boys and G be the no. of girls in survey.
so X = B + G. ---------(i)
Now since total no. of students increased by 20% , number of boys has increased by 10% & number of girls has increased by 35%.
1.2X = 1.1B + 1.35G ----(ii)

Putting value of B from (i) in (ii), we get.

1.2X = 1.1(X-G) + 1.35G --> 1.2X - 1.1X = 1.35G - 1.1G --> 0.1X = 0.25G --> G = 0.1X/0.25 = 2/5
so present percent of girls = 2/5x100 = 40
The correct answer is A.
Last edited by shashank.ism on Sun Feb 07, 2010 12:29 pm, edited 1 time in total.
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by ajith » Sun Feb 07, 2010 12:21 pm
harsh.champ wrote:In a survey, it was found that the number of students in the college has increased by 20% over the previous year. The number of boys has increased by 10%, whereas the number of girls has increased by 35%. Find out the present percentage of girls in the college.

(A)40
(B)45
(C)55
(D)75
(E)60

The correct answer is B.
say m is the num of male students and f is the no of female students

1.1m+1.35f = (m+f) 1.2

1.1 + 1.35 f/m= 1.2 + 1.2 f/m

0.15 f/m = .1
f/m = 2/3

f/(m+f ) = 2/5

% of females = 40
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by shashank.ism » Sun Feb 07, 2010 12:31 pm
harsh.champ wrote:In a survey, it was found that the number of students in the college has increased by 20% over the previous year. The number of boys has increased by 10%, whereas the number of girls has increased by 35%. Find out the present percentage of girls in the college.

(A)40
(B)45
(C)55
(D)75
(E)60

The correct answer is B.
Harsh will you please check the answer, it is coming out to be (A) i.e. 40 and you have given ans as (B) 45.
Please check the answer from the source..
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by harsh.champ » Sun Feb 07, 2010 12:57 pm
shashank.ism wrote:
harsh.champ wrote:In a survey, it was found that the number of students in the college has increased by 20% over the previous year. The number of boys has increased by 10%, whereas the number of girls has increased by 35%. Find out the present percentage of girls in the college.

(A)40
(B)45
(C)55
(D)75
(E)60

The correct answer is B.
Harsh will you please check the answer, it is coming out to be (A) i.e. 40 and you have given ans as (B) 45.
Please check the answer from the source..
___________________________________________

Hey shashank,
I have rechecked and confirmed that I have posted the correct answer.Please post your problem solving method and I can assist you.

As for ajith,
I posted this problem specifically to judge whether people can see the problem trap or not.
Your solution was somewhat like this:-

say m is the num of male students and f is the no of female students

1.1m+1.35f = (m+f) 1.2

1.1 + 1.35 f/m= 1.2 + 1.2 f/m

0.15 f/m = .1
f/m = 2/3

f/(m+f ) = 2/5

% of females = 40
Note carefully that in the problem it was asked about the present percentage,not the earlier percentage.
Just check the bold-faced equation.
To trick us ,the problem setter has kept both the options A and B.
Last edited by harsh.champ on Sun Feb 07, 2010 1:03 pm, edited 1 time in total.
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by harsh.champ » Sun Feb 07, 2010 12:59 pm
Hey shashank,
I am posting my problem approach.Just check if it matches with yours.
Let initially,no. of boys =x and no. of girls = y. Total students = x+y
Now, no. of boys= 1.1x, no. of girls = 1.35y. Total students = 1.2(x + y)
Hence, y/x = 2/3
Now, the present percentage of girls in the college is 1.35y/1.2(x + y).
Putting y=2/3 x , we get the ans. as[spoiler] 45%.[/spoiler]

I think that you also did the same mistake as ajith. What-say?
It takes time and effort to explain, so if my comment helped you please press Thanks button :)



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by shashank.ism » Sun Feb 07, 2010 1:15 pm
harsh.champ wrote:Hey shashank,
I am posting my problem approach.Just check if it matches with yours.
Let initially,no. of boys =x and no. of girls = y. Total students = x+y
Now, no. of boys= 1.1x, no. of girls = 1.35y. Total students = 1.2(x + y)
Hence, y/x = 2/3
Now, the present percentage of girls in the college is 1.35y/1.2(x + y).
Putting y=2/3 x , we get the ans. as[spoiler] 45%.[/spoiler]

I think that you also did the same mistake as ajith. What-say?
Harsh I think u took right approach in the problem. Yeah we have to calculate the present percentage
and in that case present percentage = (1.35 G/1.2X)x100 = 1.35x2/5/1.2 = (2.7/6 )x100= 45 %
(as I calculated earlier G/X=2/5)

Thanks harsh for helping us out.. This mistake in real exam could have affected a lot of my scores. Thanks a lot.
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