# Q. In a party, 75 persons took tea, 60 persons took coffee and 15 persons took both tea and coffee. No one taking milk takes tea. Each person takes at least one drink.

Question: How many persons attended the party?

Statement-1: 50 persons took milk.

Statement-2: Number of persons who attended the party is five times the number of persons who took milk only.

Which one of the following is correct in respect of the above Question and the Statements?

(a) The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone.

(b) The Question can be answered by using either Statement alone.

(c) The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.

(d) The Question cannot be answered even by using both the Statements together.

Correct Answer: (a) The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone.

#### Question from UPSC Prelims 2023 CSAT

**Explanation : **

Given Information:

## 75 persons took tea.

60 persons took coffee.

15 persons took both tea and coffee.

Analysis of the Given Information:

The number of persons who took only tea = 75 – 15 = 60.

The number of persons who took only coffee = 60 – 15 = 45.

So, the total number of persons who took tea or coffee = 60 (only tea) + 45 (only coffee) + 15 (both) = 120.

Statement-1: 50 persons took milk.

Since it’s given that no one taking milk takes tea, these 50 persons are distinct from the 120 persons who took tea or coffee.

However, this statement doesn’t provide the total number of persons attending the party since we don’t know if these 50 persons include those who took coffee, tea, or both.

Statement-2: Number of persons who attended the party is five times the number of persons who took milk only.

Let y be the number of persons who took only milk.

The total number of persons attending the party would then be 120 (those who took tea or coffee) + y.

According to the statement, this total is 5 times the number of persons who took only milk, which gives us the equation: 120 + y = 5y.

Solving this equation: 120 = 5y – y, 120 = 4y, y = 120 / 4, y = 30.

Therefore, the total number of persons attending the party is 120 + 30 = 150.

Conclusion:

Statement-1 alone is not sufficient to answer the question.

Statement-2 alone is sufficient to answer the question.