A train travelling at a speed of 55 km / hr travels from place x to place Y in 4 hours. If its speed is increased by 5 km/ hr . Then the time of journey is reduced by

Options

A. 25 minutes
B. 35 minutes
C. 20 minutes
D. 30 minutes

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Calculate the Distance
The distance traveled by the train can be calculated using the formula:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
Given that the speed of the train is 55 km/hr and the time taken is 4 hours, we can substitute these values into the formula:
\[ \text{Distance} = 55 \, \text{km/hr} \times 4 \, \text{hours} = 220 \, \text{km} \]

### Step 2: Calculate the New Speed
The new speed of the train after the increase is:
\[ \text{New Speed} = \text{Original Speed} + \text{Increase in Speed} \]
Given that the increase in speed is 5 km/hr:
\[ \text{New Speed} = 55 \, \text{km/hr} + 5 \, \text{km/hr} = 60 \, \text{km/hr} \]

### Step 3: Calculate the New Time Taken
Now, we can calculate the new time taken to travel the same distance at the new speed using the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
Substituting the distance and the new speed:
\[ \text{New Time} = \frac{220 \, \text{km}}{60 \, \text{km/hr}} = \frac{220}{60} \, \text{hours} \]
To simplify:
\[ \text{New Time} = \frac{11}{3} \, \text{hours} \approx 3.67 \, \text{hours} \text{ or } 3 \, \text{hours} \, 40 \, \text{minutes} \]

### Step 4: Calculate the Time Reduced
Now we need to find out how much time has been reduced:
\[ \text{Time Reduced} = \text{Original Time} - \text{New Time} \]
Substituting the values:
\[ \text{Time Reduced} = 4 \, \text{hours} - 3 \, \text{hours} \, 40 \, \text{minutes} \]
Converting 4 hours to minutes for easier calculation:
\[ 4 \, \text{hours} = 240 \, \text{minutes} \]
Now subtract:
\[ \text{Time Reduced} = 240 \, \text{minutes} - 220 \, \text{minutes} = 20 \, \text{minutes} \]

### Final Answer
The time of the journey is reduced by **20 minutes**.

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