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?

A. 32
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