Speed, Time and Distance
 A boy runs 20 km in 2.5 hours. How long will he take to run 32 km at double the previous speed ?

 2 hours

2 1 hours 2 
4 1 hours 2  5 hours

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The boy covers 20 km in 2.5 hours.
⇒ Speed = 20 = 8 km/hr. 2.5
New speed = 16 km/hr∴ Time = 32 = 2 hours. 16 Correct Option: A
The boy covers 20 km in 2.5 hours.
⇒ Speed = 20 = 8 km/hr. 2.5
New speed = 16 km/hr∴ Time = 32 = 2 hours. 16
 A boy goes to his school from his house at a speed of 3 km/hr and returns at a speed of 2 km/hr. If he takes 5 hours in going and coming, the distance between his house and school is :

 6 km
 5 km
 5.5 km
 6.5 km

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Let the required distance be x km.
Then,x + x = 5 3 2 ⇒ 2x + 3x = 5 6
⇒ 5x = 6 × 5∴ x = 6 × 5 = km 5
Second Method :
Here, x = 3, y = 2Average Speed = 2 × x × y x + y = 2 × 3 × 2 3 + 2 = 12 km/hr 5 Total distance = 12 × 5 = 12km 5 ∴ Required distance = 12 = 6 km 2 Correct Option: A
Let the required distance be x km.
Then,x + x = 5 3 2 ⇒ 2x + 3x = 5 6
⇒ 5x = 6 × 5∴ x = 6 × 5 = km 5
Second Method :
Here, x = 3, y = 2Average Speed = 2 × x × y x + y = 2 × 3 × 2 3 + 2 = 12 km/hr 5 Total distance = 12 × 5 = 12km 5 ∴ Required distance = 12 = 6 km 2
 A man travelled a certain distance by train at the rate of 25 kmph. and walked back at the
rate of 4 kmph. If the whole journey took 5 hours 48 minutes, the distance was

 25 km
 30 km
 20 km
 15 km

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Let the distance be x km.
Total time = 5 hours 48 minutes= 5 + 48 = 5 + 4 hours 60 5 = 29 hours 5 ∴ x + x = 29 25 4 5 ⇒ 4x + 25x = 29 100 5
⇒ 5 × 29x = 29 × 100⇒ x = 29 × 100 = 20 km. 5 × 29
Second Method :
Here, x = 25, y = 4Average speed = 2xy x + y = 2 × 25 × 4 = 200 25 + 4 29 Total Distance = 200 × 5 4 29 5 = 200 × 29 = 40 km 29 5 Correct Option: C
Let the distance be x km.
Total time = 5 hours 48 minutes= 5 + 48 = 5 + 4 hours 60 5 = 29 hours 5 ∴ x + x = 29 25 4 5 ⇒ 4x + 25x = 29 100 5
⇒ 5 × 29x = 29 × 100⇒ x = 29 × 100 = 20 km. 5 × 29
Second Method :
Here, x = 25, y = 4Average speed = 2xy x + y = 2 × 25 × 4 = 200 25 + 4 29 Total Distance = 200 × 5 4 29 5 = 200 × 29 = 40 km 29 5
 A car travelling at a speed of 40 km/hour can complete a journey in 9 hours. How long will it take to travel the same distance at 60 km/hour ?

 6 hours
 3 hours
 4 hours

4 1 hours 2

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Total distance covered
= Speed × Time
= 40 × 9 = 360 km.
The required time at 60 kmph= 360 = 6 hours. 60
Second Method :
Using Rule 9,
Here, S_{1} = 40, t_{1} = 9
S_{2} = 60, t_{2} = ?
S_{1}t_{1} = S_{2}t_{2}
40 × 9 = 60 × t_{2}t_{2} = 4 × 9 = 6 hours. 6 Correct Option: A
Total distance covered
= Speed × Time
= 40 × 9 = 360 km.
The required time at 60 kmph= 360 = 6 hours. 60
Second Method :
Using Rule 9,
Here, S_{1} = 40, t_{1} = 9
S_{2} = 60, t_{2} = ?
S_{1}t_{1} = S_{2}t_{2}
40 × 9 = 60 × t_{2}t_{2} = 4 × 9 = 6 hours. 6
 A car goes 10 metres in a second. Find its speed in km/hour.

 40
 32
 48
 36

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Speed of car = 10 m/sec.
Required speed in kmph= 10 × 18 = 36 km/hr 5 Correct Option: D
Speed of car = 10 m/sec.
Required speed in kmph= 10 × 18 = 36 km/hr 5