Roorkee express normally reaches its destination at 50 km/h in 30 hours find the speed at which it travels to reduce the time by 10 hours?

Options

A. 38 km/h
B. 76 km/h
C. 75 km/h
D. 60 km/h

Answer

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

### Step 1: Calculate the Distance
The train travels at a speed of 50 km/h for 30 hours. We can calculate the distance using the formula:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]

Substituting the values:
\[ \text{Distance} = 50 \, \text{km/h} \times 30 \, \text{hours} \]
\[ \text{Distance} = 1500 \, \text{km} \]

### Step 2: Determine the New Time
The problem states that the time is to be reduced by 10 hours. Therefore, the new time will be:
\[ \text{New Time} = 30 \, \text{hours} - 10 \, \text{hours} = 20 \, \text{hours} \]

### Step 3: Calculate the New Speed
Now that we have the distance and the new time, we can find the new speed using the formula:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]

Substituting the values:
\[ \text{Speed} = \frac{1500 \, \text{km}}{20 \, \text{hours}} \]
\[ \text{Speed} = 75 \, \text{km/h} \]

### Final Answer
The speed at which the train travels to reduce the time by 10 hours is **75 km/h**.

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