In a city `20%` of the population travels by car, `50%` by bus and `10%` travels by both car and bus. Then persons travelling by car or bus is-

Options

A. 0.8
B. 0.4
C. 0.6
D. 0.7

Answer

To solve the problem, we need to find the percentage of the population that travels by either car or bus. We can use the principle of inclusion-exclusion for this purpose.

### Step-by-Step Solution:

1. **Identify the given data:**
- Percentage of the population traveling by car (C) = 20% = 0.2
- Percentage of the population traveling by bus (B) = 50% = 0.5
- Percentage of the population traveling by both car and bus (C ∩ B) = 10% = 0.1

2. **Use the formula for union of two sets:**
The formula for the union of two sets is given by:
\[ n(C \cup B) = n(C) + n(B) - n(C \cap B) \]
where:
- \( n(C \cup B) \) = percentage of the population traveling by car or bus
- \( n(C) \) = percentage of the population traveling by car
- \( n(B) \) = percentage of the population traveling by bus
- \( n(C \cap B) \) = percentage of the population traveling by both car and bus

3. **Substitute the values into the formula:**
\[ n(C \cup B) = n(C) + n(B) - n(C \cap B) \]
\[ n(C \cup B) = 0.2 + 0.5 - 0.1 \]

4. **Perform the calculations:**
- First, add \( n(C) \) and \( n(B) \):
\[ 0.2 + 0.5 = 0.7 \]
- Then, subtract \( n(C \cap B) \):
\[ 0.7 - 0.1 = 0.6 \]

5. **Conclusion:**
The percentage of the population that travels by either car or bus is:
\[ n(C \cup B) = 0.6 = 60\% \]

### Final Answer:
60% of the population travels by car or bus.

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