Question

Excluding the halts, the speed of the bus is 50 km/ hr and including the halts it is 40 km/hr. For how many minutes does the bus stop per hour?

• A. 12
• B. 10
• C. 15
• D. 11

Answer 1

The Correct Option is A

Let's solve the problem step by step.
Given:
- Speed excluding halts: 50 km/hr
- Speed including halts: 40 km/hr
Let \( t \) be the time the bus is running (in hours) and \( s \) be the time the bus is stopped (in hours).
Since the bus stops every hour, the total distance covered in 1 hour, including halts, is equal to the distance covered without halts minus the distance lost during the halts.
The distance covered in \( t \) hours at a speed of 50 km/hr is:
\[ \text{Distance} = 50t \]
The distance covered in 1 hour at a speed of 40 km/hr is:
\[ \text{Distance} = 40 \times 1 = 40 \text{ km} \]
Equating the two distances, we get:|
\[ 50t = 40 \]
\[ t = \frac{40}{50} = 0.8 \text{ hours} \]
The bus is running for 0.8 hours, which means it stops for:
\[ 1 - 0.8 = 0.2 \text{ hours} \]
To convert the stopping time to minutes:
\[ 0.2 \text{ hours} \times 60 \text{ minutes/hour} = 12 \text{ minutes} \]
Therefore, the bus stops for:
Answer: A (12 minutes)

Answer 2

Instead of solving for the running time algebraically, we can plug each option in as the stoppage time and check which one brings the average speed down to exactly 40 km/hr.

1. Option A (12 minutes): The bus then runs for \( 60 - 12 = 48 \) minutes, or \( 0.8 \) hours, covering \( 50 \times 0.8 = 40 \) km in that 1 hour. That is exactly 40 km/hr.
2. Option B (10 minutes): Running time is 50 minutes, or \( \frac{5}{6} \) hours, covering \( 50 \times \frac{5}{6} \approx 41.7 \) km, not 40 km/hr.
3. Option C (15 minutes): Running time is 45 minutes, or \( 0.75 \) hours, covering \( 50 \times 0.75 = 37.5 \) km, not 40 km/hr.
4. Option D (11 minutes): Running time is 49 minutes, covering about \( 40.8 \) km, not 40 km/hr.

Only a 12 minute stop brings the distance covered per hour down to exactly 40 km, matching the given average speed with halts.

Let's summarize:

• The bus must cover exactly 40 km in each full hour once halts are included.
• Only a 12 minute stop, leaving 48 minutes of running at 50 km/hr, gives that 40 km.

Therefore, the correct answer is A (12 minutes).