# 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

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