There are 240 Primary 6 students. The ratio of the number of students who like Science
Q: There are 240 Primary 6 students. The ratio of the number of students who like Science to the number who do not is 5 : 3. The ratio of the number of students who like Mathematics to the number who do not is 7 : 5. The number of students who like both Science and Mathematics is 86. How many students dislike both Science and Mathematics?
B. 36
C. 40
D. 48
Answer: B
The best way to solve this is to use a Venn diagram:
Now we can write down some sums:
If the number of students who like science divided by the number of students who do not is 5/3, then 5/8 of the total like science and 3/8 don’t. Since the total number of students is 240, then the number who like science is (5/8) x 240 = 150
So, the number of students who like only science = 150 – 86 = 64
Likewise the number of students who like Mathematics = (7/12) x 240 = 140
So, the number of students who like only Mathematics = 140 – 86 = 54
And the number of students who dislike both Science and Mathematics is therefore 240 – (64 + 86 + 54) = 36