A car travels from city A to city B at an average speed of 60 km/hr and reaches city B on time. If the car reduces its speed to 50 km/hr, it takes 16 minutes more to reach city B. What is the distance between city A and city-B ? (In kilometer)

Options

A. 80
B. 85
C. 82
D. 84

Answer

To solve the problem, we need to find the distance between city A and city B based on the information given about the speeds and the time taken.

### Step-by-Step Solution:

1. **Identify the speeds and the time difference**:
- Speed from A to B = 60 km/hr
- Reduced speed = 50 km/hr
- Time difference when speed is reduced = 16 minutes

2. **Convert the time difference from minutes to hours**:
- 16 minutes = 16/60 hours = 4/15 hours

3. **Let the distance between city A and city B be \( D \) kilometers**.

4. **Calculate the time taken to travel the distance at both speeds**:
- Time taken at 60 km/hr = \( \frac{D}{60} \) hours
- Time taken at 50 km/hr = \( \frac{D}{50} \) hours

5. **Set up the equation based on the time difference**:
- The time taken at 50 km/hr is 16 minutes (or \( \frac{4}{15} \) hours) more than the time taken at 60 km/hr.
- Therefore, we can write the equation:
\[ \frac{D}{50} - \frac{D}{60} = \frac{4}{15} \]

6. **Find a common denominator to solve the equation**:
- The least common multiple of 50 and 60 is 300.
- Rewrite the equation:
\[ \frac{6D}{300} - \frac{5D}{300} = \frac{4}{15} \]
- This simplifies to:
\[ \frac{D}{300} = \frac{4}{15} \]

7. **Cross-multiply to solve for \( D \)**:
- Multiply both sides by 300:
\[ D = 300 \times \frac{4}{15} \]
- Simplifying this gives:
\[ D = 20 \times 4 = 80 \text{ km} \]

8. **Conclusion**:
- The distance between city A and city B is **80 kilometers**.