Quants Questions : Time and Distance Set 13

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Questions Penned by Yogit

1. Excluding stoppages, a train can travel with a speed of 60km/hr but with stoppages it can travel at an average 45km/hr. For how many minutes the train stops in one hour.
   a) 10min
   b) 12min
   c) 15min
   d) 18min
   e) None of these
   

   Answer & Explanation

   Answer – c) 15min
   Explanation :
   due to stoppages 15km less is travel by train so,
   15 = 60*t, t = 15 minutes – train stops in one hour
   
   
   
2. Two trains are travelling towards each other. The distance between the trains initially is 400km. After some time they meet at a distance of 150 km from one end. Find the ratio of the speed of the trains.
   a) 2:5
   b) 3:5
   c) 4:7
   d) 7:3
   e) 3:7
   e) None of these
   

   Answer & Explanation

   Answer – b) 3:5
   Explanation :
   At some tine T they meet each other so,
   150/a = 250/b (a and b are the speeds of the train respectively)
   So, a:b = 3:5
   
   
   
3. A thief steals a car at 3 pm and drives at 75 km/hr. He got discovered by the police at 4 pm Then the police start chasing him in another car travelling at 100km/hr. When will the policeman catch the thief?
   a) 5pm
   b) 6pm
   c) 7pm
   d) 8pm
   e) None of these
   

   Answer & Explanation

   Answer – c) 7pm
   Explanation :
   In one hour thief will travel 75 km. Now let after x distance thief get caught, then
   x/75 = (75+x)/100
   u will get x = 225, so to travel 225 + 75 = 300 km by police, he will take 3 hours i.e at 7 pm
   
   
   
4. A journey of 800 km is done in a total of 10 hours, If 320 km is travel by train and remaining by bus. The same journey is done in 8 hours if 240 km is travel by train and remaining is done by bus. Find the ratio of the speed of train to bus.
   a) 2:11
   b) 3:11
   c) 1:11
   d) 4:11
   e) None of these
   

   Answer & Explanation

   Answer – c) 1:11
   Explanation :
   10 = 320/st + 480/sb  and
   8 = 240/st + 560/sb
   st and sb are the speeds of train and bus respectively
   
   
   
5. If a man walks to his office at 5km/hr, he will be late by 30 minutes. If he walks at 6km/hr, he will be
   late by 10minutes. Find the distance between his home and office?
   a) 5km
   b) 10km
   c) 15km
   d) 20km
   e) None of these
   

   Answer & Explanation

   Answer – b) 10km
   Explanation :
   Let distance be D km, then,
   D = 5*(t + 1/2) and D = 6*(t+ 1/6) solve both question and we get D = 10km
   
   
   
6. Rakesh travelled 1800 kilometre by air which formed 3/5 of the total journey. He travels 1/4 of the trip by car and the remaining trip by train. Find the distance travelled by train.
   a) 350
   b) 450
   c) 550
   d) 650
   e) None of these
   

   Answer & Explanation

   Answer – b) 450
   Explanation :
   3/5 of D = 1800. So D = 3000 km,
   so distance travelled by train = 3000 – 1800 – 1/4 of 3000 = 450
   
   
   
7. Arya starts cycling along the boundaries of the squares. She starts from a point A and after 90 minutes she reached to point C diagonally opposite to A. If she is travelling with 20km/hr, then find the area of square field.
   a) 125
   b) 225
   c) 325
   d) 425
   e) None of these
   

   Answer & Explanation

   Answer – b) 225
   Explanation :
   D = 20*3/2 = 30 km. So side of square is 15km, so area – 225km^2
   
   
   
8. The distance between two cities P and Q is 300km. A train starts from station P at 10 am with speed 80 km/hr towards Q. Another train starts from Q towards P with speed 40km/hr at 11 am . At what time do they meet?
   a) 12.20pm
   b) 12.40 pm
   c) 12.50 pm
   d) 1 pm
   e) None of these
   

   Answer & Explanation

   Answer – c) 12.50 pm
   Explanation :
   First train starts at 10am so in one hour it covers 80 km in one hour. Now distance b/w P and Q is 220. Suppose at some’ x’ km they meet. So,
   x/80 = (220-x)/40
   x = 440/3. The time after which they meet = (440/3)/80 = 11/6 i.e = 1hr 50 min.
   
   
   
9. A walks with a speed of 6 km/hr and after 5 hr of his start, B starts running towards A at a speed of 8 km/hr. At what distance from start will B catch A.
   a) 100
   b) 110
   c) 120
   d) 140
   e) None of these
   

   Answer & Explanation

   Answer – c) 120
   Explanation :
   In 5hrs, A will cover 30 km. Now, at some distance ‘x’. So A will cover X distance and B will cover 30 + X.
   x/6 = (30+x)/8
   x = 90. So distance from start after which B will catch A = 120km
   
   
   
10. Two guns were fired from the same place at an interval of 13 minutes but a person travelling in a train approaching the place hear the second sound after 12 minutes than the first. Find the speed of the train. Consider sound travels at a speed of 330 meter per sec.
    a) 33km/hr
    b) 66km/hr
    c) 99km/hr
    d) 120km/hr
    e) None of these
    

    Answer & Explanation

    Answer – c) 99km/hr
    Explanation :
    Sound travels at 330m/sec. In one minute sound travel = 330*60 meter.
    So speed of train = (330*60)/720 = 330/12 m/sec or 330/12 of 18/5 = 99 km/hr