220 students were asked if they liked chocolate or vanilla ice cream.140 said they liked chocolate and 120 said they liked vanilla. how many students liked both chocolate and vanilla?

Let x represent the number of students who liked both chocolate and vanilla ice cream. With this, the number of students who liked chocolate ice cream alone is 140 - x. Similarly, the number of students who liked vanilla ice cream only is 120 - x. The total number of students is 220. 
                            x + (140 - x) + (120 - x) = 220

The value of x is 40. Thus, 40 students liked both chocolate and vanilla.