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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.** 2 mins

**b.** 1.5 mins

**c.** 1⅕ mins

**d.** 2.5 mins

**e.** None of these

**Answer & Explanation**

**Answer : [C]**

Explanation :

⇒ Raman’s speed = 20 km/hr = 20 × 5/18 = 50/9 m/sec

⇒ 400 × 9/50 = 1⅕ mins

**2- John travelled from his town to city. 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. **15 km

**b.** 22 km

**c.**20 km

**d.**25 km

**Answer & Explanation**

**Answer : [C]**

- Average speed of John = 2xy/x+y = 2 × 25 × 4 / 25 + 4= 200/29 km/h
- Distance traveled = Speed × Time = 200/29 × 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.**150 m

**b.**250 m

**c.**200 m

**d.**300 m

**Answer : [C]**

Explanation :

⇒ Lenght of train = 20 × 10 = 200 meters

**4-Ram walks at a speed of 12 km/h. Today the day was very hot so walked at ⅚ 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. 40 mins
b. 45 mins
c. 50 mins
d. 60 mins
**

**Answer & Explanation**

**Answer : [C]**

Explanation :

- If Ram is walking at ⅚ 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 ?**

**a.** 72 mins

**b.** 78 mins

**c.** 76 mins

**d.** None of these

**Answer & Explanation**

**Answer : [B]**

⇒Reduced speed = 65-15 = 50 km/h

⇒ Now car will take 65/50 × 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 ?**

**a.** 1 m/s

**b.** 1.33 m/s

**c.** 1.25 m/s

**d.**1.5 m/s

**Answer & Explanation**

**Answer : [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