45 percent of students in a school are girls. Among the students who

Question

45 percent of students in a school are girls. Among the students who have travelled abroad earlier, 25% are girls and among the ones who have not, 25% are boys. If the difference between the number of students who have travelled outside the country and the number of students who have not is 120, what is the total number of students in that school?

A) 360
B) 480
C) 500
D) 600
E) 720

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Official Answer

D

A) 360
B) 480
C) 500
D) 600
E) 720

mayuresh0307 · Answer

This is how i solved,

Total who travelled = X
Girls who travelled = X/4

Total who did not travel = Y
Girls who did not travel = 3Y/4

Difference between travelled and not travelled = 120
X-Y = 120
X = 120+ Y

Total girls = (X/4 + 3Y/4) = 0.45*(X+Y)

substitute X = 120 + Y

((120+Y+3Y)/4) = 0.45*( 120+Y+Y)

30+Y = 54 + 0.9Y

0.1Y = 24

Y = 240

Thus, X = 240+120 = 360

Total students = 240+360 = 600.

Kinshook · Answer

Given: 45 percent of students in a school are girls. Among the students who have travelled abroad earlier, 25% are girls and among the ones who have not, 25% are boys.

Asked: If the difference between the number of students who have travelled outside the country and the number of students who have not is 120, what is the total number of students in that school?

Boys  Girls  Total  
  Travelled abroad  75y  25y  100y  
  Not Travelled abroad  25z  75z  100z  
  Total  55x=55(y+z)  45x=45(y+z)  100x=100(y+z)

|100y - 100z| = 120
|y-z| = 1.2

100y + 100z = 100x
y + z = x

75y + 25z = 55(y+z)
20y = 30z
y = 1.5z
x = 2.5z
|100y - 100z| = 120
|y-z| = 1.2
1.5z - z = .5z = 1.2
z = 1.2/.5 = 2.4
y = 3.6
x = 6
Total number of students = 100x = 600

Boys  Girls  Total  
  Travelled abroad  270  90  360  
  Not Travelled abroad  60  180  240  
  Total  330  270  600

IMO D

sivatx2 · Answer

total students = x
girls = 0.45x
boys = 0.55x -----(1)

Let y, is the total number of boys & girls who went abroad.
Then, the number of boys & girls who didn't go abroad, n = x-y 
=> Based on given information
|x-y -y| = 120 => x-2y = 120 or 2y-x = 120 -----(2)

girls who went abroad = 0.25y
boys who went abroad = 0.75y ------(3)

Also, boys who did not go abroad = 0.25(x-y) -----(4)
girls who did not go abroad = 0.75(x-y)

boys = boys who went abroad + boys who did not go abroad
Using (1),(3) & (4),

0.55x = 0.75y + 0.25(x-y)
0.3x = 0.5y
3x = 5y 
y = (3/5)x -----(3)

From(2), 
2y -x = 120 
Substituting (3) in (2)

6x/5 - x = 120

x/5 = 120
x= 600
Therefore the total number of students in school is 600.
Hence D is the correct answer choice.

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45 percent of students in a school are girls. Among the students who

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	Boys	Girls	Total
Travelled abroad	75y	25y	100y
Not Travelled abroad	25z	75z	100z
Total	55x=55(y+z)	45x=45(y+z)	100x=100(y+z)

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45 percent of students in a school are girls. Among the students who

Prep Toolkit

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My Rewards