Maths-6 Time and Distance: Questions and Step-by-Step Solutions for Competitive Exams (SSC, BSSC, Bank, Railways)

Maths-6 Time and Distance: Questions and Step-by-Step Solutions for Competitive Exams (SSC, BSSC, Bank, Railways)

Time and Distance from the very basics. This topic is a staple in competitive exams like CDS, SSC, UPSC, and once you master the core formulas and logic, you’ll solve these questions quickly and confidently.

Core Concept: Time and Distance

🔹 Basic Formula

Distance = Speed × Time

From this, you can derive:

• Speed = Distance\Time
• Time = Distance\Speed

Units to Remember

Step-by-Step Examples

1. Basic Speed Calculation

Q: A car travels 120 km in 3 hours. What is its speed?

Solution:
Speed = Distance ÷ Time = 120/3 = 40 ) km/hr ✅

2. Time Calculation

Q: A train travels at 60 km/hr. How long will it take to cover 180 km?

Solution:
Time = Distance ÷ Speed = 180/60 = 3  hours ✅

3. Distance Calculation

Q: A person walks at 5 km/hr for 2 hours. How far does he walk?

Solution:
Distance = Speed × Time = ( 5 × 2 = 10 ) km ✅

4. Convert Speed Units

Q: Convert 72 km/hr to m/s

Solution:
72 × 5/18 = 20 ) m/s ✅

5. Relative Speed (Same Direction)

Q: Two trains move in the same direction at 60 km/hr and 40 km/hr. What is their relative speed?

Solution:
Relative speed = 60 – 40 = 20 km/hr ✅

6. Relative Speed (Opposite Direction)

Q: Two trains move in opposite directions at 60 km/hr and 40 km/hr. What is their relative speed?

Solution:
Relative speed = 60 + 40 = 100 km/hr ✅

7. Time to Cross a Pole

Q: A train 120 meters long moves at 36 km/hr. How much time to cross a pole?

Step 1: Convert speed to m/s → 36 × 5/18 = 10 ) m/s
Step 2: Time = Distance ÷ Speed = 120/10 = 12 ) seconds ✅

8. Time to Cross a Platform

Q: Train length = 120 m, Platform length = 80 m, Speed = 36 km/hr
Solution:
Total distance = 120 + 80 = 200 m
Speed = 10 m/s → Time = 200/10 = 20 seconds ✅

9: Average Speed

If a vehicle travels the same distance at speeds (x) and (y),
Average Speed} = 2xy/ (x+y)

✔ Example: 60 km at 30 km/hr and return 60 km at 60 km/hr.
Average speed = 2 x30 x 60/ (30+60) = 40 km/hr.

10: Boats and Streams

• Downstream speed = (Boat speed + Stream speed).
• Upstream speed = (Boat speed – Stream speed).
• Use same distance formula: Distance = Speed × Time.

Tips to Solve Faster

• Always convert km/hr to m/s when the distance is in meters.
• Use relative speed when two objects move toward or away from each other.
• For crossing problems, total distance = length of train + length of object (pole/platform/bridge).
• Practice unit conversions and mental division for speed.

Quick Practice (Basic)

1. A bike runs at 40 km/hr for 3 hours. Find the distance covered.
2. Convert 54 km/hr into m/s.
3. A train 180 m long passes a pole in 12 seconds. Find its speed in km/hr.
4. Two cars move in opposite directions with speeds of 40 and 50 km/hr. Find their relative speed.
5. A boat can row 12 km/hr in still water. If the stream speed is 3 km/hr, find the downstream and upstream speed.