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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, 06:48
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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, 08:00
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, 10:37
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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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Re: In a certain class, 3/10 of the boys and 4/10 of the girls walk  [#permalink]

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New post 21 Jan 2019, 10:54
assuming the total no of student to be 100 (using smart no. approach since 100 will be divisible by both 10 and 25 i.e denominator)
Let the no. of boys be b and no. of girls be g. we know b+g=100 ....(i)
Additionally, we also know
3/10(b)+4/10(g)=9/25(b+g)
0.3b+0.4g=36 (we know the value of b+g) ....(ii)

we have 2 equation and 2 variable.
multiplying eq (i) by 0.3 and subtracting from equation 2 will give:

0.3b+0.3g=30
0.3b+0.4g=36

0.1g=-6

g=60

Substituting value of g in equation (ii)

4/10(60)=24

SO the fraction of girls that walk to the school is 24/100 i.e 6/25
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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 23 Jun 2019, 03:11
Let, Total no. of students= 100 and Total no. of girls= x
Then,
Total no. of boys= 100 - x
According to question,
Girls who walk to school= 4/10 of Total no. of girls = (4/10) * x = 4x/10
Boys who walk to school = 3/10 of Total no. of boys = (3/10) * (100-x) = 30 - 3x/10
Students who walk to school = 9/25 of Total no. of students = (9/25) * 100 = 36
Therefore,
30 – (3x/10) + (4x/10) = 36
=> x/10 = 36-30
=> x = 6 * 10 = 60
We know,
Girls who walk to school= 4x/10 = 4/10 * 60 = 24
So,
Fraction of girls who walk to school = 24/100 = 6/25

Hence option(c)
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Re: In a certain class, 3/10 of the boys and 4/10 of the girls walk   [#permalink] 23 Jun 2019, 03:11
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