Speed, Time and Distance
 When Alisha goes by car at 50 kmph, she reaches her office 5 minutes late. But when she takes her motorbike, she reaches 3 minutes early. If her office is 25 kms away, what is the approximate average speed at which she rides her motorbike ?

 68 kmph
 62 kmph
 58 kmph
 52 kmph

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Difference of time = 5 + 3 = 8 minutes
= 8 hour = 2 hour 60 15
If the speed of motorbike be x kmph, then25 − 25 = 2 50 x 15 ⇒ 25 = 1 − 2 x 2 15 ⇒ 25 = 15 − 4 = 11 x 30 30
⇒ 11x = 25 × 30⇒ x = 25 × 30 11 = 750 = 68.18 kmph 11
≈ 68 kmphCorrect Option: A
Difference of time = 5 + 3 = 8 minutes
= 8 hour = 2 hour 60 15
If the speed of motorbike be x kmph, then25 − 25 = 2 50 x 15 ⇒ 25 = 1 − 2 x 2 15 ⇒ 25 = 15 − 4 = 11 x 30 30
⇒ 11x = 25 × 30⇒ x = 25 × 30 11 = 750 = 68.18 kmph 11
≈ 68 kmph
 A man covers a total distance of 100 km on bicycle. For the first 2 hours, the speed was 20 km/hr and for the rest of the journey, it came down to 10 km/hr. The average speed will be


12 1 km/hr 2  13 km/hr

15 1 km/hr 8  20 km/hr


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Distance covered in first 2 hours
= 2 × 20 = 40 km.
Remaining distance
= 100 – 40 = 60 km.
Time taken in covering 60 km at 10 kmph= 60 = 6 hours 10 ∴ Required average speed = Total distance Total Time = 100 kmph 2 + 6 = 100 kmph 8 = 25 kmph 2 = 12 1 kmph 2 Correct Option: A
Distance covered in first 2 hours
= 2 × 20 = 40 km.
Remaining distance
= 100 – 40 = 60 km.
Time taken in covering 60 km at 10 kmph= 60 = 6 hours 10 ∴ Required average speed = Total distance Total Time = 100 kmph 2 + 6 = 100 kmph 8 = 25 kmph 2 = 12 1 kmph 2
 A train travels 500 m in first minute. In the next 4 minutes, it travels in each minute 125 m more than that in the previous minute. The average speed per hour of the train during those 5 minutes will be

 30 km/hr
 45 km/hr
 50 km/hr
 55 km/hr

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Total distance covered by train in 5 minutes
= (500 + 625 + 750 + 875 + 1000) metre = 3750 metre
= 3.75 km.Time = 5 minutes = 5 hour 60 = 1 hour 12 Speed of train = Distance Time = 3.75 kmph (1/12)
= (3.75 × 12) kmph
= 45 kmphCorrect Option: B
Total distance covered by train in 5 minutes
= (500 + 625 + 750 + 875 + 1000) metre = 3750 metre
= 3.75 km.Time = 5 minutes = 5 hour 60 = 1 hour 12 Speed of train = Distance Time = 3.75 kmph (1/12)
= (3.75 × 12) kmph
= 45 kmph
 A train runs at an average speed of 75 km/hr. If the distance to be covered is 1050 kms, how long will the train take to cover it ?

 13 hrs
 12 hrs
 15 hrs
 14 hrs

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Time = Distance Speed = 1050 = 14 hours 75 Correct Option: D
Time = Distance Speed = 1050 = 14 hours 75
 A man walks from his house at an average speed of 5 km per hour and reaches his office 6 minutes late. If he walks at an average speed of 6 km/h he reaches 2 minutes early. The distance of the office from his house is

 6 km
 9 km
 12 km
 4 km

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Required distance of office from house = x km. (let)
Time = Distance Speed
∴ According to the question,x − x = 6 + 2 = 2 5 6 60 15 ⇒ 6x − 5x 30 = 2 15 ⇒ x = 2 30 15 ⇒ x = 2 × 30 = 4 km. 15
Second Method :
Here, S_{1} = 5, t_{1} = 6
S_{2} = 6, t_{2} = 2Distance = (S_{1} × S_{2})(t_{1} + t_{2}) S_{2} − S_{1} = (5 × 6)(6 + 2) 6 − 5 = 30 × 8 = 4 km. 60 Correct Option: D
Required distance of office from house = x km. (let)
Time = Distance Speed
∴ According to the question,x − x = 6 + 2 = 2 5 6 60 15 ⇒ 6x − 5x 30 = 2 15 ⇒ x = 2 30 15 ⇒ x = 2 × 30 = 4 km. 15
Second Method :
Here, S_{1} = 5, t_{1} = 6
S_{2} = 6, t_{2} = 2Distance = (S_{1} × S_{2})(t_{1} + t_{2}) S_{2} − S_{1} = (5 × 6)(6 + 2) 6 − 5 = 30 × 8 = 4 km. 60