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In a certain boys camp, 20% of the total boys are from

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In a certain boys camp, 20% of the total boys are from  [#permalink]

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New post 19 Aug 2014, 06:41
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In a certain boys camp, 20% of the total boys are from school A and 30% of those study science. If there are 49 boys in the camp that are from school A but do not study science then what is the total number of boys in the camp?

A. 70
B. 245
C. 150
D. 35
E. 350

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Re: In a certain boys camp, 20% of the total boys are from  [#permalink]

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New post 19 Aug 2014, 07:28
benjamin09 wrote:
In a certain boys camp, 20% of the total boys are from school A and 30% of those study science. If there are 49 boys in the camp that are from school A but do not study science then what is the total number of boys in the camp?

A. 70
B. 245
C. 150
D. 35
E. 350


Since 30% of the boys from school A study science, then 70% of the boys from school A do NOT study science and since 20% of the total number of boys are from school A, then 0.2*0.7 = 0.14, or 14% of the boys in the camp are from school A and do not study science.

We are told that this number equals to 49, so 0.14*{total} = 49 --> {total} = 350.

Answer: E.
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Re: In a certain boys camp, 20% of the total boys are from  [#permalink]

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New post 19 Aug 2014, 23:08
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Refer diagram below
Attachment:
scie.png
scie.png [ 4.76 KiB | Viewed 4106 times ]

Lets say total number of students = x

From School A\(= \frac{20x}{100}\)

30% from School A study science\(= \frac{20x}{100} * \frac{30}{100} = \frac{6x}{100}\)

Remaining from School A not studying science\(= \frac{20x}{100} - \frac{6x}{100} = \frac{14x}{100}\)

Given that \(\frac{14x}{100} = 49\)

x = 350

Answer = E
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Re: In a certain boys camp, 20% of the total boys are from  [#permalink]

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New post 19 Aug 2014, 23:12
Thanks a lot Bunuel & Paresh.
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Re: In a certain boys camp, 20% of the total boys are from  [#permalink]

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New post 11 Jan 2019, 11:33
Let the total boys in camp=100
Boys from School A=20*100/100=20
Boys from school A which study science= 3*20/100=6
Boys from school A which do not study Science=20-6=14

Now, by unitary method,
No. of boys in camp=100*49/14=350
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Re: In a certain boys camp, 20% of the total boys are from   [#permalink] 11 Jan 2019, 11:33
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