The distance between two points A and is covered in `5 (1)/(2)` hours at a speed of 50 km/hr. If the speed is increased by 5km/hr how much time would be saved ?
A. 5 minutes
B. 15 minutes
C. 50 minutes
D. 30 minutes

Options

A. A
B. D
C. B
D. C

Answer

To solve the problem step by step, let's break it down:

### Step 1: Calculate the Distance
The distance between points A and B can be calculated using the formula:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]

Given:
- Speed = 50 km/hr
- Time = \( 5 \frac{1}{2} \) hours = \( 5.5 \) hours

Now, substituting the values:
\[ \text{Distance} = 50 \, \text{km/hr} \times 5.5 \, \text{hours} \]
\[ \text{Distance} = 50 \times \frac{11}{2} \]
\[ \text{Distance} = 50 \times 5.5 = 275 \, \text{km} \]

### Step 2: Calculate the New Speed
If the speed is increased by 5 km/hr, the new speed will be:
\[ \text{New Speed} = 50 \, \text{km/hr} + 5 \, \text{km/hr} = 55 \, \text{km/hr} \]

### Step 3: Calculate the Time Taken at New Speed
Now, we need to calculate the time taken to cover the same distance at the new speed using the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]

Substituting the distance and new speed:
\[ \text{Time} = \frac{275 \, \text{km}}{55 \, \text{km/hr}} \]
\[ \text{Time} = 5 \, \text{hours} \]

### Step 4: Calculate the Time Saved
Now, we compare the original time taken with the new time taken:
- Original Time = \( 5.5 \) hours
- New Time = \( 5 \) hours

Time saved:
\[ \text{Time Saved} = \text{Original Time} - \text{New Time} \]
\[ \text{Time Saved} = 5.5 \, \text{hours} - 5 \, \text{hours} = 0.5 \, \text{hours} \]

### Step 5: Convert Time Saved to Minutes
To convert hours into minutes:
\[ \text{Time Saved in Minutes} = 0.5 \, \text{hours} \times 60 \, \text{minutes/hour} = 30 \, \text{minutes} \]

### Final Answer
The time saved is **30 minutes**.