Directions for questions 28–31: Read the passage below and solve the questions based on it.
5% of the passengers do not like coffee, tea and lassi and 10% like all the three, 20% like coffee and tea, 25% like lassi and coffee and 25% like lassi and tea. 55% like coffee, 50% like tea, and 50% like lassi.
The percentage of passengers who like both tea and lassi but not coffee, is

Options

A. `15`
B. `25`
C. `40`
D. `75`

Answer

To solve the problem, we will use a Venn diagram to organize the information given about the passengers' preferences for coffee, tea, and lassi.

### Step-by-Step Solution:

1. **Identify the Total Percentages**:
- We know that 5% of the passengers do not like any of the drinks. Therefore, 95% of the passengers like at least one of the drinks.

2. **Set Up the Venn Diagram**:
- We will create three circles representing coffee (C), tea (T), and lassi (L).

3. **Fill in the Known Values**:
- 10% of passengers like all three drinks (C ∩ T ∩ L).
- 20% like both coffee and tea (C ∩ T).
- 25% like both lassi and coffee (L ∩ C).
- 25% like both lassi and tea (L ∩ T).
- 55% like coffee (C).
- 50% like tea (T).
- 50% like lassi (L).

4. **Calculate Intersections**:
- For coffee and tea (C ∩ T):
- We already have 10% who like all three, so the percentage who like only coffee and tea is:
\[ (C \cap T) - (C \cap T \cap L) = 20\% - 10\% = 10\% \]
- For lassi and coffee (L ∩ C):
- Similarly, we find:
\[ (L \cap C) - (C \cap T \cap L) = 25\% - 10\% = 15\% \]
- For lassi and tea (L ∩ T):
- We calculate:
\[ (L \cap T) - (C \cap T \cap L) = 25\% - 10\% = 15\% \]

5. **Calculate Individual Preferences**:
- For coffee (C):
- Total liking coffee = 55%
- Used: 10% (all three) + 10% (only coffee and tea) + 15% (only lassi and coffee) = 35%
- Remaining for only coffee:
\[ 55\% - 35\% = 20\% \]
- For tea (T):
- Total liking tea = 50%
- Used: 10% + 10% + 15% = 35%
- Remaining for only tea:
\[ 50\% - 35\% = 15\% \]
- For lassi (L):
- Total liking lassi = 50%
- Used: 10% + 15% + 15% = 40%
- Remaining for only lassi:
\[ 50\% - 40\% = 10\% \]

6. **Find the Required Percentage**:
- We need the percentage of passengers who like both tea and lassi but not coffee:
- This is the value we calculated for L ∩ T excluding those who like coffee:
\[ L \cap T - (C \cap T \cap L) = 15\% - 10\% = 15\% \]

### Final Answer:
The percentage of passengers who like both tea and lassi but not coffee is **15%**.