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In a certain class, 3/10 of the boys and 4/10 of the girls walk

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In a certain class, 3/10 of the boys and 4/10 of the girls walk  [#permalink]

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New post 08 Jan 2019, 05:48
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Question Stats:

77% (02:11) correct 23% (02:08) wrong based on 13 sessions

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In a certain class, 3/10 of the boys and 4/10 of the girls walk to school. If 9/25 of the students walk to school, what fraction of the students are girls and walk to school?

A. 1/5

B. 4/15

C. 6/25

D. 8/25

E. 3/2

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Re: In a certain class, 3/10 of the boys and 4/10 of the girls walk  [#permalink]

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New post 08 Jan 2019, 07:00
rohan2345 wrote:
In a certain class, 3/10 of the boys and 4/10 of the girls walk to school. If 9/25 of the students walk to school, what fraction of the students are girls and walk to school?

A. 1/5

B. 4/15

C. 6/25

D. 8/25

E. 3/2


Good question, Here is my approach

Let Boys be x and Girls be y, WTS - Walk to school

Total students x+y

----------------B---------------G----------------Total
WTS--------(3/10)*x-------(4/10) * y-------(9/25) * (x+y)
----------------x----------------y---------------x + y

To find \(\frac{G(WTS)}{Total(WTS)}\)
\(\frac{3}{10}\)*x + \(\frac{4}{10}\) * y = \(\frac{9}{25}\) * (x+y)
Solving above will give
3x=2y
\(\frac{x}{y}\) = \(\frac{2}{3}\)

x = \(\frac{2y}{3}\)

\(\frac{G(WTS)}{Total(WTS)}\)

=> \(\frac{4y}{10}\) * \(\frac{3}{5y}\)
=> \(\frac{6}{25}\)

Correct Answer C
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In a certain class, 3/10 of the boys and 4/10 of the girls walk  [#permalink]

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New post 08 Jan 2019, 09:37
Let the total number of Girls be G and Boys be B

Total number of students = B + G

Fraction of Girls walking to school = 4G/10 ----- (i)
Fraction of Boys walking to school = 3B/10 ----- (ii)

Fraction of students walking to school = 9(Total)/25 = 9(B+G)/25 ----- (iii)

eq(i) + eq(ii) = eq(iii)

=> 4G/10 + 3B/10 = (9B + 9G)/25
Solving, we get
B = \(\frac{2G}{3}\) -----(iv)


Now, the ratio of girls walking to school to the total number of students
\(\frac{(4G|10)}{(B+G)}\)

from (iv)
=> \(\frac{(4G|10)}{(2G|3 + G)}\)
=> \(\frac{12}{50}\)
=> \(\frac{6}{25}\)

Answer: (C)
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In a certain class, 3/10 of the boys and 4/10 of the girls walk &nbs [#permalink] 08 Jan 2019, 09:37
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