# Arithmetic Aptitude :: Time and Distance

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A person crosses a 600 m long street in 5 minutes. What is his speed in km per hour?

A3.6

B7.2

C8.4

D10

Explanation:

Speed = 600/(5*60) m/sec. = 600/300 m/sec = 2 m/sec
Now convert m/sec to km/hr
= 2 x 18/5 km/hr = 7.2 km/hr.

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How Many minutes does shyam take to cover a distance of 500 m, if he runs at a speed of 20km/h?

A1 min 30 sec.

B1 min 25 sec.

C1 min.

D1 min 10 sec

Explanation:

Ram's speed = 20 km/h = (20 * 5/18) m/sec. =50/9 m/sec.

Formula Used: Time = Distance/Speed.

Time taken to cover 500m = 500/(50/9) sec

= (500 *9)/50 sec = 90 sec = 1 min 30 sec..

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An Athlete runs 200 metres race in 24 seconds. His speed is:

A20 km/hr

B24 kim/hr

C28.5 km/hr

D30 km/hr

Explanation:

Speed = (200/24) m/sec = 25/3 m/sec
convert m/sec to km/hr
(25/3 * 18/5) km/hr = 30 km/hr.

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Albert is travelling on his cycle and has calculated to reach point A at 2 P.M. if he travels at 10 kmph, he will reach there at 12 noon if he travels at 15 kmph. At what speed must he travel to reach A at 1 P.M.?

A8 kmph

B11 kmph

C12 kmph

D14 kmph

Explanation:

Let's Assume the distance travelled Albert = x km.
Formula Used: Time = Distance/Speed
so (x/10 - x/15) = 2 hrs
=> (3x - 2x)/30 = 2 hrs.
=> (3x - 2x) = 60
x = 60 km.

Time taken to travel 60 km at 10 km/hr = 60/10 hrs = 6 hrs.
Formula Used: Speed = Distance/Time
So, Albert started 6 hours before 2 P.M. i.e @ 8 A.M.

Required speed = 60/5 kmph. = 12 kmph.

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Raghav had to walk a certain distance. He walked half the distance at a speed of 4 km/hour and the remaining half at a speed of 5 km/hour. If the total time taken was 9 hour, the distance was

A9 km

B20 km

C40 km

D50 km

Explanation:

Let half of the distance travelled be d.
Time taken at the speed of 4 km/hr = (d/4)
Time taken at the speed of 5 km/hr = (d/5)
Therefore, total time = (d/4) + (d/5) = 9 hrs.
? (5d + 4d)/20 = 9
? 9d = 180
? d = 20.
Therefore total distance = d x 2 = 40 kms

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Virat travelled 75 kms in 7 hours. He went some distance at the rate of 12 km/hr and the rest at 10 km/hr. How far did he travel at the rate of 12 km/hr?

A30 kms

B25 kms

C40 kms

D35 kms.

Explanation:

Let the distance travelled at the rate of 12 kmph be x km
Time taken to travel this distance = x/12 .......(1)
Then the distance travelled at the rate of 10 km/hr will be (75 - x)
Time taken to travel this distance = (75 - x)/10 .......(2)
Total time taken to cover the total distance = 7 hrs
=>(x/12) + (75 - x)/10 = 7 [sum of (1) and (2)]
=> (10x + 900 - 12x) = 840
=> -2x = -60
=> x = 30.
Therefore, the distance travelled at the rate of 12 km/hr = 30km.

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A boy rides his bicycle 10 kms at an average speed of 12 kmph and again travels 12 kms at an average speed of 10 kmph. His average speed for the entire trip is approximately:

A10.4 kmph

B10.8 kmph

C11.0 kmph

D12.2 kmph

Explanation:

Average speed is represented by total distance divided by the time taken.
Total distance = 10 kms + 12 kms = 22 kms
Total Time = (10/12) + (12/10)
? (10/12) + (12/10) = (100 + 144)/120 = 244/120 hrs
Average speed = 22/(244/120) = 10.8 kmph.
Average speed for the entire trip is 10.8 kmph.

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An athlete runs half of the distance at the speed of 10 km/hr and remaining 15 km at the speed of 20 km/hr, how much time will be taken to cover the total distance?

A95 mins

B135 mins

C120 mins

D115 mins.

Explanation:

We know that time = distance/speed
Time taken by the athlete for the first half = 15/10
And time taken by the athlete for the second half = 15/20
Total time = 15/10 + 15/20 = (45/20) x 60 = 135 mins
Time taken to cover the total distance is 135 mins.

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A person travelled by train for 1 hour at a speed of 50 kmph. He then travelled by a taxi for 30 minutes at a speed of 32 kmph to complete his journey. What is the average speed at which he travelled during the journey?

A44 kmph

B42 kmph

C41 kmph

D33 kmph

Explanation:

Total distance travelled in 1 hour
= 50 + (&frac; x 32) km
= 66 km
? Average speed = Total distance/Total time
= 66/(3/2) = 44 kmph.

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A car covers four successive 6 km stretches at speeds of 25 kmph, 50 kmph, 75 kmph and 150 kmph respectively. Its average speed over this distance is

A25 kmph

B50 kmph

C75 kmph

D50 kmph

Explanation:

Time = Distance/Speed
Time taken for each 6 km can be given by
6/25, 6/50, 6/75 and 6/150
Total time = (6/25) + (6/50) + (6/75) + (6/150) = (36 + 18 + 12 + 6)/150 = 72/150
Average speed = Distance/time = (24/72) x 150 = 50 kmph

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