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

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BSchool Forum Moderator
Joined: 29 Jan 2015
Posts: 1446
Location: India
WE: General Management (Non-Profit and Government)
In a certain class, 3/10 of the boys and 4/10 of the girls walk  [#permalink]

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08 Jan 2019, 06:48
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00:00

Difficulty:

65% (hard)

Question Stats:

60% (02:55) correct 40% (03:23) wrong based on 55 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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Director
Joined: 09 Mar 2018
Posts: 994
Location: India
Re: In a certain class, 3/10 of the boys and 4/10 of the girls walk  [#permalink]

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08 Jan 2019, 08:00
1
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 = $$\frac{2y}{3}$$

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

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

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Intern
Joined: 24 Oct 2017
Posts: 5
GMAT 1: 620 Q49 V25
In a certain class, 3/10 of the boys and 4/10 of the girls walk  [#permalink]

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08 Jan 2019, 10:37
1
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)
=> $$\frac{(4G|10)}{(2G|3 + G)}$$
=> $$\frac{12}{50}$$
=> $$\frac{6}{25}$$

Intern
Joined: 03 Jan 2017
Posts: 21
Location: India
Concentration: Finance, Economics
Re: In a certain class, 3/10 of the boys and 4/10 of the girls walk  [#permalink]

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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)
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
Intern
Joined: 16 Feb 2019
Posts: 7
Re: In a certain class, 3/10 of the boys and 4/10 of the girls walk  [#permalink]

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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)
Intern
Joined: 16 Mar 2019
Posts: 3
Re: In a certain class, 3/10 of the boys and 4/10 of the girls walk  [#permalink]

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20 Oct 2019, 02:49
1
Applying method of allegation,

3/10............4/10
.......9/5........
2/50............3/50
2................3

ratio of boys to girls = 2:3

total student : girl = 5:3
= 5 : 3*(4/10)
= 5 : 6/5
= 25: 6

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Re: In a certain class, 3/10 of the boys and 4/10 of the girls walk   [#permalink] 20 Oct 2019, 02:49
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