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08 Oct 2021, 04:54
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Difficulty:
75%
(hard)
Question Stats:
62% (03:12) correct
38%
(03:21)
wrong
based on 108
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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
A) 360
B) 480
C) 500
D) 600
E) 720
08 Oct 2021, 05:01
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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.
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.
08 Oct 2021, 09:14
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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?
|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
IMO D
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
