CAMANISHPARMAR wrote:
There are 816 students in enrolled at a certain high school. Each of these students is taking at least one of the subjects economics, geography, and biology. The sum of the number of students taking exactly one of these subjects and the number of students taking all 3 of these subjects is 5 times the number of students taking exactly 2 of these subjects. The ratio of the number of students taking only the two subjects economics and geography to the number of students taking only the two subjects economics and biology to the number of students taking only the two subjects geography and biology is 3:6:8. How many of the students enrolled at this high school are taking only the two subjects geography and biology?
A) 35
B) 42
C) 64
D) 136
E) 240
Let,
a = # of students enrolled only in Economics
b = # of students enrolled only in Geography
c = # of students enrolled only in Biology
d = # of students enrolled only in Economics & Geography
e = # of students enrolled only in Economics & Biology
f = # of students enrolled only in Biology & Geography
g = # of students enrolled in all three
Total # of students = 816 = a+b+c+d+e+f+g
Now given that, (a+b+c)+g = 5(d+e+f)
Therefore we get 6(d+e+f) = 816
d+e+f = 136
Now also given that d:e:f = 3:6:8
Hence, d+e+f = 3x+6x+8x = 17x
Therefore, 17x = 136
x = 136/17
Now we need # of students enrolled only in Biology & Geography = 8x = 8*(136/17) = 64.
Answer C.
Thanks,
GyM
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