A bus runs at 50 kmph. If the speed is increased by 10 kmph it will cover 20 km more in the same time. Find the actual distance covered ?

Options

A. 100 km
B. 150 km
C. 200 km
D. 250 km

Answer

To solve the problem step by step, we can use the relationship between distance, speed, and time.

### Step 1: Define the variables
Let the actual distance covered by the bus be \( x \) kilometers. The speed of the bus is initially 50 km/h.

### Step 2: Write the time taken for the initial distance
The time taken to cover the distance \( x \) at a speed of 50 km/h can be expressed as:
\[ \text{Time} = \frac{x}{50} \]

### Step 3: Write the time taken for the increased speed
If the speed is increased by 10 km/h, the new speed becomes 60 km/h. The distance covered in this case is \( x + 20 \) kilometers. The time taken to cover this distance is:
\[ \text{Time} = \frac{x + 20}{60} \]

### Step 4: Set the times equal to each other
Since the time taken is the same in both cases, we can set the two expressions for time equal to each other:
\[ \frac{x}{50} = \frac{x + 20}{60} \]

### Step 5: Cross-multiply to eliminate the fractions
Cross-multiplying gives us:
\[ 60x = 50(x + 20) \]

### Step 6: Expand and simplify the equation
Expanding the right side:
\[ 60x = 50x + 1000 \]
Now, subtract \( 50x \) from both sides:
\[ 10x = 1000 \]

### Step 7: Solve for \( x \)
Dividing both sides by 10:
\[ x = 100 \]

### Conclusion
The actual distance covered by the bus is \( 100 \) kilometers.