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 passengers who like only coffee is greater than the passengers who like only lassi by

Options

A. A) 25%
B. B) 100%
C. C) 75%
D. D) 0%

Answer

To solve the problem step by step, we will use the information provided about the preferences of the passengers regarding coffee, tea, and lassi. We will use a Venn diagram approach to visualize the relationships and calculate the required percentages.

### Step 1: Identify the total percentages and relationships
- Total percentage of passengers = 100%
- Percentage of passengers who do not like any of the three drinks = 5%
- Therefore, the percentage of passengers who like at least one of the drinks = 100% - 5% = 95%

### Step 2: Set up the known values
- Let:
- \( A \) = percentage of passengers who like coffee = 55%
- \( B \) = percentage of passengers who like tea = 50%
- \( C \) = percentage of passengers who like lassi = 50%

- Intersections:
- \( |A \cap B \cap C| \) = percentage who like all three = 10%
- \( |A \cap B| \) = percentage who like coffee and tea = 20%
- \( |A \cap C| \) = percentage who like coffee and lassi = 25%
- \( |B \cap C| \) = percentage who like tea and lassi = 25%

### Step 3: Calculate the exclusive preferences
1. **Coffee and Tea only**:
\[ |A \cap B| - |A \cap B \cap C| = 20\% - 10\% = 10\% \]

2. **Coffee and Lassi only**:
\[ |A \cap C| - |A \cap B \cap C| = 25\% - 10\% = 15\% \]

3. **Tea and Lassi only**:
\[ |B \cap C| - |A \cap B \cap C| = 25\% - 10\% = 15\% \]

### Step 4: Calculate the percentages for only coffee, only tea, and only lassi
1. **Only Coffee**:
\[ |A| - (|A \cap B| + |A \cap C| - |A \cap B \cap C|) = 55\% - (10\% + 15\% + 10\%) = 55\% - 35\% = 20\% \]

2. **Only Tea**:
\[ |B| - (|A \cap B| + |B \cap C| - |A \cap B \cap C|) = 50\% - (10\% + 15\% + 10\%) = 50\% - 35\% = 15\% \]

3. **Only Lassi**:
\[ |C| - (|A \cap C| + |B \cap C| - |A \cap B \cap C|) = 50\% - (15\% + 15\% + 10\%) = 50\% - 40\% = 10\% \]

### Step 5: Compare the percentages of only coffee and only lassi
- Only Coffee = 20%
- Only Lassi = 10%

### Step 6: Calculate the difference
- The difference in percentage between passengers who like only coffee and those who like only lassi:
\[ 20\% - 10\% = 10\% \]

### Final Answer
The passengers who like only coffee is greater than the passengers who like only lassi by **10%**.

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