A train travels a certain distance with out stoppages with an average speed of 90 km/hr, but with stop-pages at an average speed of 80 km/hr. The number of minutes per hour that the train stops is:

Options

A. `13(1)/(3)` min
B. 12 min
C. 8 min
D. `6(2)/(3)` min

Answer

To solve the problem step by step, we will use the formula that relates the speeds of the train with and without stoppages to find out how many minutes per hour the train stops.

### Step 1: Understand the given speeds
- The speed of the train without stoppages (S1) = 90 km/hr
- The speed of the train with stoppages (S2) = 80 km/hr

### Step 2: Use the formula
We can use the formula to find the time the train stops per hour:
\[ \text{Time stopped per hour} = \left( \frac{S1 - S2}{S1} \right) \times 60 \]
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:
\[ \text{Time stopped per hour} = \left( \frac{90 - 80}{90} \right) \times 60 \]

### Step 4: Simplify the expression
Calculate the difference in speeds:
\[ 90 - 80 = 10 \]
Now substitute back into the formula:
\[ \text{Time stopped per hour} = \left( \frac{10}{90} \right) \times 60 \]

### Step 5: Calculate the fraction
Now simplify \( \frac{10}{90} \):
\[ \frac{10}{90} = \frac{1}{9} \]
So the equation becomes:
\[ \text{Time stopped per hour} = \frac{1}{9} \times 60 \]

### Step 6: Perform the multiplication
Calculating \( \frac{1}{9} \times 60 \):
\[ \text{Time stopped per hour} = \frac{60}{9} = 6.67 \text{ minutes} \]

### Final Answer
The train stops approximately **6.67 minutes per hour**.

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