Speed, Time and Distance
 A man completes 30 km of a journey at the speed of 6 km/hr and the remaining 40 km of the journey in 5 hours. His average speed for the whole journey is

 7 km/hr

6 4 km/hr 11  8 km/hr
 7.5 km/hr

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Time taken to cover 30km at 6 kmph = 30 = 5 hours 6
Time taken to cover 40 km = 5 hours∴ Average speed = Total distance Time taken = 30 + 40 10 = 70 = 7 kmph 10 Correct Option: A
Time taken to cover 30km at 6 kmph = 30 = 5 hours 6
Time taken to cover 40 km = 5 hours∴ Average speed = Total distance Time taken = 30 + 40 10 = 70 = 7 kmph 10
 One third of a certain journey is covered at the rate of 25 km/hour, onefourth at the rate of 30 km/hour and the rest at 50 km/hour. The average speed for the whole journey is

 35 km/hour

33 1 km/hr 3  30 km/hour

37 1 km/hr 12

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Let the total distance be x km.
Total time = x x 5x 3 + 4 + 12 25 30 50 = x + x + x 75 120 120 = x + x 75 60 = 4x + 5x = 3x hours 300 100 ∴ Average speed = Total distance Time taken
=x 3x 100 = 100 = 33 1 kmph 3 3
Second Method :
Here, x = 3, u = 25, y = 4, v = 30z = 12 , w = 50 5 Average Speed = 1 1 + 1 + 1 xu yv zw = 1 1 + 1 + 1 3 × 25 4 × 30 (12/5) × 50 = 1 1 + 1 + 1 75 120 120 = 1 1 + 1 75 60
=1 4 + 5 300 = 300 = 100 9 3 = 33 1 km/hr. 3 Correct Option: B
Let the total distance be x km.
Total time = x x 5x 3 + 4 + 12 25 30 50 = x + x + x 75 120 120 = x + x 75 60 = 4x + 5x = 3x hours 300 100 ∴ Average speed = Total distance Time taken
=x 3x 100 = 100 = 33 1 kmph 3 3
Second Method :
Here, x = 3, u = 25, y = 4, v = 30z = 12 , w = 50 5 Average Speed = 1 1 + 1 + 1 xu yv zw = 1 1 + 1 + 1 3 × 25 4 × 30 (12/5) × 50 = 1 1 + 1 + 1 75 120 120 = 1 1 + 1 75 60
=1 4 + 5 300 = 300 = 100 9 3 = 33 1 km/hr. 3
 A man goes from a place A to B at a speed of 12 km/hr and returns from B to A at a speed of 18 km/hr. The average speed for the whole journey is


14 2 km/hr 5  15 km/hr

15 1 km/hr 2  16 km/hr


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Average speed = 2xy kmph x + y = 2 × 12 × 18 kmph 12 + 18 = 2 × 12 × 18 kmph 30 = 14 2 kmph 5 Correct Option: B
Average speed = 2xy kmph x + y = 2 × 12 × 18 kmph 12 + 18 = 2 × 12 × 18 kmph 30 = 14 2 kmph 5
 A man goes from Mysore to Bangalore at a uniform speed of 40 km/hr and comes back to
Mysore at a uniform speed of 60 km/hr. His average speed for the whole journey is

 48 km/hr
 50 km/hr
 54 km/hr
 55 km/hr

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Average speed = 2xy kmph x + y = 2 × 40 × 60 kmph 40 + 60
= 48 kmphCorrect Option: A
Average speed = 2xy kmph x + y = 2 × 40 × 60 kmph 40 + 60
= 48 kmph
 A person went from A to B at an average speed of x km/hr and returned from B to A at an average speed of y km/hr. What was his average speed during the total journey ?


x + y 2xy 
2xy x + y 
2 x + y 
1 + 1 x y


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Required average speed = 2xy kmph x + y
[Since, can be given as corollary If the distance between A and B be z units, thenAverage speed = Total distance Time taken = z + z z + z x y = 2 1 + 1 x y = 2 x + y xy = 2xy x + y Correct Option: B
Required average speed = 2xy kmph x + y
[Since, can be given as corollary If the distance between A and B be z units, thenAverage speed = Total distance Time taken = z + z z + z x y = 2 1 + 1 x y = 2 x + y xy = 2xy x + y