Quantitative Aptitude: Time, Speed and Distance Set 13

1. A covers 1/3rd of his journey at the speed of 15km/hr and half of the rest of the journey at the speed of 20 km/hr and rest at the speed of 25km/hr. What is the average speed of A?
   A) 12 1/2
   B) 16 3/14
   C) 19 7/47
   D) 15 2/5
   E) None
   
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   Option C
   Solution:
   Let total distance 3x
   Total time=x/15 + x/20 + x/25
   Average speed =Total distance /Total time
   =3x/ ( x/15 + x/20 + x/25)
   =3x/(20x+15x+12x/300)
   = (3x*300)/ 47x=900/47=19 7/47.
2. Two person A and B started from two different places towards each other. If the ratio of their speeds be 6:11, then what is the ratio of distance covered by A and B respectively till the point of meeting?
   A) 1:5
   B) 6:11
   C) 4:9
   D) 5:12
   E) None
   
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   Option B
   Solution:
   When time is constant the distance covered by A and B will be in the ratio of their speeds.
   i.e. ratio of distance is 6:11 as time is constant.
3. The speeds of Noel and Joel are 30 km/h and 40 km/h. Initially Joel is at a place X and Noel is at a place Y. The distance between X and Y is 650 km. Noel started his journey 3 hours earlier than Joel to meet each other. If they meet each other at a place Z somewhere between X and Y, then the distance between Z and Y is:
   A) 420km
   B) 290km
   C) 360km
   D) 330km
   E) None
   
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   Option D
   Solution:
   Distance between X and Y 650km.
   In 3 hrs noel covered 3*30=90km.
   Then only Joel starts.
   Their meeting time be =560(650-90)/70(30+40) =8hrs.
   Distance between Y and Z=(8*30)+90=330km.
4. A Man standing on a railway platform observe that a train going in one direction takes 6 second to pass him. Another train of same length going in opposite direction takes 5 seconds to pass him. The time taken (in seconds) by two train to cross each other will be:
   A) 55sec
   B) 44/9sec
   C) 60/11sec
   D) 39sec
   E) None
   
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   Option C
   Solution:
   Let length of each train be X m, then
   S1 = X/6 and S2 = X/5.
   Time = {2x/[(X/6)+(X/5)]}
   = 60/11 seconds.
5. In every 30 min the time of a watch increases by 3 min. After setting the correct time at 7 am. What time will the watch show after 4 hrs?
   A) 11.24am
   B) 11.45am
   C) 11.35am
   D) 11.20am
   E) None
   
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   Option A
   Solution:
   Every 30min it increases 3min
   In 1hour the time is = 2 * 3 = 6.min
   After 4hour the time is = 4 * 6 = 24.
   The time after 4hrs is 7+4 =11hr + 24 min.==> 11.24am
6. A train can travel 50% faster than a car. Both start from point A at the same time and reach point B 75 kms away from A at the same time. On the way, however, the train lost about 12.5 minutes while stopping at the stations. The speed of the train is:
   A) 120km/hr
   B) 150km/hr
   C) 180km/hr
   D) 90km/hr
   E) None
   
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   Option C
   Solution:
   Speed Ratio Car :Train =100:150==>2:3
   Then 75/2x- 75/3x =12.5/60
   750=12.5x
   ==>x=60.
   The speed of the train =3*60=180km/hr.
7. A runs twice as fast as B and B runs thrice as fast as C. The distance covered by C in 90 minutes, will be covered by A in
   A) 15min
   B) 20min
   C) 22min
   D) 24min
   E) None
   
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   Option A
   Solution:
   Ratio of the speed of A, B and C = 6:3:1
   Then, ratio of time taken;
   = 1/6:1/3:1 = 1:2:6;
   Hence, time taken by A = 90/6 *1= 15 minutes.
8. A thief is noticed by a policeman from a distance of 200 m. The thief starts running and the policeman chases him. The thief and the policeman run at the rate of 10 km and 11 km per hour respectively. What is the distance between them after 6 minutes?
   A) 180m
   B) 150m
   C) 130m
   D) 100m
   E) None
   
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   Option D
   Solution:
   Relative speed = (11 – 10) km/hr = 1 km/hr
   Distance covered in 6 minutes =(1/60)*6=1/10km=100m.
   Distance between the thief and policeman = (200 – 100) m = 100 m.
9. If A travels to his school from his house at the speed of 4 km/h, then he reaches the school 8 minutes late. If he travels at the speed of 5 km/h, he reaches the school 7 minutes earlier than school time. The distance of his school from his house is:
   A) 3km
   B) 5km
   C) 2km
   D) 6km
   E) None
   
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   Option B
   Solution:
   Let the distance between school and home be x km.
   The difference of time is (7+8)15 min = 15/60 hour.
   Now,
   (x/4)-(x/5)= 15/60
   x/20 = 1/4
   x = 5km.
10. Two boys starting from the same place walk at a rate of 5kmph and 5.5kmph respectively. What time will they take to be 8.5km apart, if they walk in the same direction?
    A) 12hrs
    B) 14hrs
    C) 15hrs
    D) 17hrs
    E) None
    
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    Option D
    Solution:
    The relative speed of the boys = 5.5kmph – 5kmph
    = 0.5 kmph
    Distance between them is 8.5 km
    Time = Distance/Speed
    Time= 8.5km / 0.5 kmph = 17 hrs .

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