Excluding stoppages, the speed of a train is 48 km/hr and including stoppages it is 40 km/hr. What is the stoppages time of the train (in minutes) per hour?

Options

A. 12
B. 14
C. 20
D. 10

Answer

To solve the problem, we need to determine the stoppage time of the train per hour based on the given speeds. Here’s a step-by-step breakdown of the solution:

### Step 1: Identify the given speeds
- Speed excluding stoppages (S1) = 48 km/hr
- Speed including stoppages (S2) = 40 km/hr

### Step 2: Use the formula to calculate stoppage time
The formula to calculate the stoppage time per hour is:
\[ \text{Stoppage Time} = \frac{S1 - S2}{S1} \times 60 \]
Where:
- \(S1\) is the speed without stoppages
- \(S2\) is the speed with stoppages

### Step 3: Substitute the values into the formula
Substituting the values we have:
\[ \text{Stoppage Time} = \frac{48 - 40}{48} \times 60 \]

### Step 4: Simplify the calculation
First, calculate the difference in speeds:
\[ 48 - 40 = 8 \]
Now substitute this back into the equation:
\[ \text{Stoppage Time} = \frac{8}{48} \times 60 \]

### Step 5: Simplify the fraction
\[ \frac{8}{48} = \frac{1}{6} \]
Now substitute this back into the equation:
\[ \text{Stoppage Time} = \frac{1}{6} \times 60 \]

### Step 6: Calculate the stoppage time
\[ \text{Stoppage Time} = 10 \text{ minutes} \]

### Final Answer
The stoppage time of the train per hour is **10 minutes**.

---