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?
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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NA
SHSTTON
30
Solv. Corr.
39
Solv. In. Corr.
69
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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:
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.
Workspace
NA
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41
Solv. Corr.
29
Solv. In. Corr.
70
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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?
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.
Workspace
NA
SHSTTON
9
Solv. Corr.
44
Solv. In. Corr.
53
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A man covered a certain distance at some speed. Had he moved 3 kmph faster, he would have taken 40 minutes less. If he had moved 2 kmph slower, he would have taken 40 minutes more. The distance (in km) is:
And, x/(y-2) - x/y = 40/60
y(y - 2) = 3x ....(ii)
By Solving (i) by (ii), we get: x = 40
Workspace
NA
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17
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29
Solv. In. Corr.
46
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Sanu travelled a distance of 20 kms at the speed of 5 km/hr, he reached 40 minutes late. If he had walked at the speed of 8 km/hr, how early from fixed time will he reach?
Time taken to travel 20 kms at the speed of 5 kmph.
=> t = 20/5 = 4 hrs.
Actual time of reaching = (4 hrs - 40 mins) = 3 hrs 20 mins ......(1)
Time taken to travel 20 kms at the speed of 8 kmph.
=> t = 20/8 = 2.5 hrs. ......(2)
Difference between (1) and (2) => (3 hrs 20 mins - 2 hrs 30 mins)
(200 mins - 150 mins) = 50 mins.
Sanu would have reached 50 mins earlier.
Workspace
NA
SHSTTON
24
Solv. Corr.
39
Solv. In. Corr.
63
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0 M:45 S
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A thief steals a car at 2.30 p.m and drives it at 60 kmph. The theft is discovered at 3 p.m and the owner sets off in another car at 75 kmph. When will be overtake the thief.
As Theft is discovered at 3:00pm but Thief stole the car at 2:30.
This means thief covered some distance in this 30 min gap.
Distance travelled by thief in 30 min = 60 * 1/2 = 30 km
Owner Discovered Car at 3:00pm
Now relative speed = (75-60)km/hr = 15km/hr
Time needed to travel 30km by the speed of 15km/hr.
Time at which owner meets thief = 30/15 = 2 hrs
So After 2 hrs (i.e,at 5:00 pm) the owner will catch/overtake the thief
Workspace
NA
SHSTTON
8
Solv. Corr.
42
Solv. In. Corr.
50
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0 M:33 S
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Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour?
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