There are 210 persons in a party, and all of them eat three different types of flavoured icecreams. 40 people eat only butterscotch, 30 people eat all three flavoured icecream,there are total 130 people who eat butterscotch and 100 people who eat vanila. 4 0 people eat butterscotch and vanila only, 10 people eat chocolate and vanila only.

People eating chocolate and butterscotch only are what percent of people eating only butterscotch?

The correct answer is 50%.

Let us break down the given data into three sets representing the three flavours of ice cream:
Let $B$ be the set of people who eat Butterscotch,
Let $V$ be the set of people who eat Vanilla, and
Let $C$ be the set of people who eat Chocolate.

From the given problem, we have the following values:

• Total number of persons in the party = 210
• People who eat only Butterscotch = 40
• People who eat all three flavours (Butterscotch, Vanilla, and Chocolate) = 30
• Total people who eat Butterscotch, $n\left(B\right)$ = 130
• Total people who eat Vanilla, $n\left(V\right)$ = 100
• People who eat Butterscotch and Vanilla only = 40
• People who eat Chocolate and Vanilla only = 10

Let us find the number of people who eat Chocolate and Butterscotch only.

The total number of people who eat Butterscotch, $n\left(B\right)$, consists of four regions:

1. People who eat only Butterscotch
2. People who eat Butterscotch and Vanilla only
3. People who eat all three flavours
4. People who eat Chocolate and Butterscotch only

Substituting the known values into this relationship:

$130=40+40+30+\text{(People who eat Chocolate and Butterscotch only)}$

$130=110+\text{(People who eat Chocolate and Butterscotch only)}$

$\text{People who eat Chocolate and Butterscotch only}=130-110=20$

Now, we need to find what percent the people eating Chocolate and Butterscotch only are of the people eating only Butterscotch:

$\text{Required Percentage}=\left(\frac{\text{People eating Chocolate and Butterscotch only}}{\text{People eating only Butterscotch}}\right)\times 100$

$\text{Required Percentage}=\left(\frac{20}{40}\right)\times 100=50\%$

Hence, the people eating Chocolate and Butterscotch only are 50% of the people eating only Butterscotch.