Question

Of the students who eat in a certain cafeteria, each student either likes or dislikes lima beans and each student either likes or dislikes brussels sprouts. Of these students, \small \frac{2}{3} dislike lima beans; and of those who dislike lima beans, \small \frac{3}{5} also dislike brussels sprouts. How many of the students like brussels sprouts but dislike lima beans

(1) 120 students eat in the cafeteria
(2) 40 of the students like lima beans

Answer 1

Answer: There are 32 students who like brussels sprouts but dislike beans.

Explanation:

Since we have given that

Number of students eat in the cafeteria = 120

Fraction dislike lime beans =
`(2)/(3)`

Fraction who dislike lime beans and brussles sprouts both =
`(2)/(3)* (3)/(5)`

Fraction who dislikes lime beans but not brussles is given by

`(2)/(3)(1-(3)/(5))\\\\=(2)/(3)* (2)/(5)\\\\=(4)/(15)`

So, Number of students who like brussels sprouts but dislike lima beans is given by

`(4)/(15)* 120\\\\=32`

Hence, there are 32 students who like brussels sprouts but dislike beans.