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### Time & Distance Problem with Solution

**1- How many minutes Raman will take to cover a distance of 400 meters if he runs at a speed of 20 km/hr ?**

**a.**Â 2 mins

**b.**Â 1.5 mins

**c.**Â 1â…• mins

**d.**Â 2.5 mins

**e.** None of these

**Answer & Explanation**

**AnswerÂ :Â [C]**

ExplanationÂ :

â‡’ Raman’s speed = 20 km/hr = 20 Ã— 5/18 = 50/9 m/sec

â‡’ 400 Ã— 9/50 = 1â…• mins

**2- John travelled from his town to city. Â John went to city by bicycle at the speed of 25 km/h and came back at the speed of 4 km/h. If John took 5 hours and 48 min to complete his journey, what is the distance between town and city ?**

**a.Â **15 km

**b.**Â 22 km

**c.Â**20 km

**d.**Â 25 km

**Answer & Explanation**

**AnswerÂ :Â [C]**

- Average speed of John = 2xy/x+y =Â Â 2 Ã— 25 Ã— 4 / 25 + 4= 200/29 km/h
- Distance traveled = Speed Ã— Time = 200/29 Ã— 29/5 = 40 Km
- Distance between city and town = 40/2 = 20 km

**3- Speed of a train is 20 meters per second. It can cross a pole in 10 seconds. What is the length of train ?**

**a.Â**150 m

**b.Â**250 m

**c.Â**200 m

**d.Â**300 m

**AnswerÂ :Â [C]**

ExplanationÂ :

â‡’ Lenght of train = 20 Ã— 10 = 200 meters

**4-Ram walks at a speed of Â 12 km/h. Today the day was very hot so walked at â…š of his average speed. He arrived his school 10 minutes late. Find the usual time he takes to cover the distance between his school and home?**

**a.Â 40 mins
b.Â 45 mins
c.Â 50 mins
d.Â 60 mins
**

**Answer & Explanation**

**AnswerÂ :Â [C]**

ExplanationÂ :

- If Ram is walking at â…š Â of his usual speed that means he is taking 6/5 of using time.
- 6/5 of usual time – usual time = 10 mins
- 1/5 of usual time = 10 mins
- Usual time = 50 mins

**Answer & Explanation**

5-

**A car running at 65 km/h takes one hour to cover a distance. If the speed is reduced by 15 km/hour then in how much time it will cover the distance Â ?**

**a.**Â 72 mins

**b.**Â 78 mins

**c.**Â 76 mins

**d.**Â None of these

**Answer & Explanation**

**AnswerÂ :Â [B]**

â‡’Reduced speed = 65-15 = 50 km/h

â‡’ Now car will take 65/50 Ã— 60 mins = 78 mins

**6-In a 100 m race A runs at a speed of 1.66 m/s. If A gives a start of 4m to B and still beats him by 12 seconds. What is the speed of B Â ?**

**a.**Â 1 m/s

**b.**Â 1.33 m/s

**c.**Â 1.25 m/s

**d.Â**1.5 m/s

**Answer & Explanation**

**AnswerÂ :Â [B]**

- Time is taken by A to cover 100 meters = 60 seconds
- Since A gives a start of 4 seconds then time takes by B = 72 seconds
- B takes 72 seconds to cover 96 meters
- Speed of B = 96/72 = 1.33 m/s