Yogesh can run 1 km in 6 min 20 s and Vijay can cover the same distance in 6min 40s. By what distance can Yogesh beat Vijay?

Options

A. 50 m
B. 90 m
C. 45 m
D. 30 m

Answer

To solve the problem of how much distance Yogesh can beat Vijay by, we will follow these steps:

### Step 1: Convert the running times into hours
Yogesh's time to run 1 km is 6 minutes and 20 seconds.
- Convert this into hours:
- 6 minutes = 6/60 hours = 1/10 hours
- 20 seconds = 20/3600 hours = 1/180 hours
- Total time for Yogesh = 1/10 + 1/180
- To add these fractions, find a common denominator:
- The least common multiple of 10 and 180 is 180.
- Convert 1/10 to have a denominator of 180: (1/10) * (18/18) = 18/180
- Now add: 18/180 + 1/180 = 19/180 hours

Vijay's time to run 1 km is 6 minutes and 40 seconds.
- Convert this into hours:
- 6 minutes = 6/60 hours = 1/10 hours
- 40 seconds = 40/3600 hours = 1/90 hours
- Total time for Vijay = 1/10 + 1/90
- The least common multiple of 10 and 90 is 90.
- Convert 1/10 to have a denominator of 90: (1/10) * (9/9) = 9/90
- Now add: 9/90 + 1/90 = 10/90 = 1/9 hours

### Step 2: Calculate the speeds of Yogesh and Vijay
- Speed is calculated as distance/time.
- For Yogesh:
- Speed = Distance / Time = 1 km / (19/180 hours) = 1 * (180/19) km/h = 180/19 km/h
- For Vijay:
- Speed = Distance / Time = 1 km / (1/9 hours) = 1 * 9 km/h = 9 km/h

### Step 3: Determine how far Vijay runs while Yogesh finishes the race
- When Yogesh finishes 1 km, we need to find out how far Vijay has run in the same time.
- Time taken by Yogesh to run 1 km = 19/180 hours.
- Distance covered by Vijay in that time = Speed × Time = 9 km/h × (19/180 hours) = (9 * 19) / 180 km = 171 / 180 km = 19 / 20 km.

### Step 4: Calculate the distance by which Yogesh beats Vijay
- The distance Yogesh beats Vijay by = Distance run by Yogesh - Distance run by Vijay = 1 km - (19/20 km) = (20/20 km - 19/20 km) = 1/20 km.

### Step 5: Convert the distance into meters
- 1 km = 1000 meters, so:
- (1/20) km = (1000/20) meters = 50 meters.

### Final Answer
Yogesh can beat Vijay by **50 meters**.

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