Quants Questions : Time and Distance Set 14

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Questions Penned by Yogit

1. A car after travelling 100 km from point A meets with an accident and then proceeds at 3/4 of its original speed and arrives at the point B 90 minutes late. If the car meets the accident 60 km further on, it would have reached 15 minutes sooner. Find the original speed of the train?
   a) 60km/hr
   b) 80km/hr
   c) 100km/hr
   d) 120km/hr
   e) None of these
   
   Answer & Explanation

   Answer –b) 80km/hr
   Explanation :
   let distance between A and B be D km and real speed of the car be S km/hr
   First time car takes 90 minutes more and second time car takes 75 minutes more than scheduled time.
   So, T1 – T2 = 15/60 = 100
   15/60 = [100/s + (D -100)/(3s/4)] – [160/s + (D – 160)/(3s/4)] Solve this D will be cancelled and S comes out to be 80km/hr
   
2. A boy goes to school from his home at a speed of 4 km/hr and returns at a speed of 6 km/hr. If in total he took 5 hours in going and coming back, the distance between his house and school?
   a) 8km
   b) 10km
   c) 12km
   d) 14km
   e) None of these
   
   Answer & Explanation

   Answer –c) 12km
   Explanation :
   5 = d/4 + d/6 (d is the distance between school and home)
   
3. A police officer is 110 meter behind a thief. The officer runs 21 meters and thief runs 14 meters in a minute. In what time the officer will catch the thief ?
   a) 15.3/7 minutes
   b) 15.5/7 minutes
   c) 15.1/7 minutes
   d) 16.3/7 minutes
   e) None of these
   
   Answer & Explanation

   Answer –b) 15.5/7 minutes
   Explanation :
   let the thief covers x more distance before get caught, so officer have to cover 110+x in the same time in which thief covers x distance ,
   x/14 = (110 +x)/21, x = 220 so time = 330/21 = 110/7 = 15.5/7 minutes
   
4. Two trains P and Q are separated by 220 km on a straight line. One train starts at 8 am from one station A towards B at 40 km/hr and another train starts from B towards A at 9 am at 60 km/hr. At what time will both train will meet?
   a) 10:00 am
   b) 10:30 am
   c) 10:48 am
   d) 11:00 am
   e) None of these
   
   Answer & Explanation

   Answer –c) 10:48 am
   Explanation :
   In one hour first train will cover 40 km, so distance between them remains only 180. Now
   x/40 = (180 –x)/60, we get x = 72, so time = 72/40 = 1 hour 48 minutes
   so both will meet at 10:48 am
   
5. Two girls begin together to write out a book containing 900 lines. The first girl starts with the first line, writing at a speed of 150 lines per hour and the second girl starts writing from the last line at the rate of 200 lines per hour. At which line will they meet?
   a) 384^th line
   b) 386^th line
   c) 389^th line
   d) 400^th line
   e) None of these
   
   Answer & Explanation

   Answer –b) 386^th line
   Explanation :
   Solve this question as analogous to distance method,
   At some x page they will meet, so
   x/150 = (900 – x)/200, we get x = 385.7 = 386^th line (approx.)
   
6. Two women start walking towards each other at same time from two points separated by 84 km. First women walks at 5km/hr and second walks at 2 km/hr in the first hour, 2.5 km/hr in second hour, 3 km/hr in third hour and so on. Find the approximate time after which both women will meet?
   a) 8hr
   b) 9hr
   c) 10hr
   d) 11hr
   e) None of these
   
   Answer & Explanation

   Answer –b) 9hr
   Explanation :
   Let after T time both women meet each other, so distance travelled by first women is 5T and second women forms an AP, so
   distance = (T/2)*[4 + (T -1)1/2] so, 5T + (T/2)*[4 + (T -1)1/2] = 84, solve for T, u will get T = 9 hrs
   take √2073 = 45 (approx.)
   
7. Two places are A and B are 200 kms from each other. A train leaves from A for B at the same time another train leaves B for A. The two trains meet at the end of 8 hours. If the train travelling from A to B travels 10km/hr faster than the other. Find the speed of the faster train?
   a) 15 km/hr
   b) 16 km/hr
   c) 17.5 km/hr
   d) 18 km/hr
   e) None of these
   
   Answer & Explanation

   Answer –c) 17.5 km/hr
   Explanation :
   speed of trains  = s + 10 and s km/hr. At some P distance from A both train will meet. So,
   8 = P/(s +10) = (200 – P)/s
   Solve both equation, we get s = 7.5 so faster train speed 17.5 km/hr
   
8. Two bullets are fired at an interval of 15 minutes but a car approaching the place of firing hears the second bullet after 14 minutes. Speed of sound is 330 meters per second. Find the speed of the car?
   a) 80km/hr
   b) 82km/hr
   c) 85km/hr
   d) 90km/hr
   e) None of these
   
   Answer & Explanation

   Answer –c) 85km/hr
   Explanation :
   distance travels by sound in one minute is equal to the distance travels by car in 14 minutes i.e. 60*330 = s*14*60
   s = (330/14)*(18/5) = 85km/hr (approx.)
   
9. A truck driving on a highway passed a man walking at the rate of 12km/hr in the same direction. He could see the truck for 2 minutes and up to 500 meters. Find the speed of the truck?
   a) 27km/hr
   b) 30km/hr
   c) 32km/hr
   d) 42km/hr
   e) None of these
   
   Answer & Explanation

   Answer – a) 27km/hr
   Explanation :
   500 = (s – 12*5/18)*2*60
   s = 27km/hr
   
10. Excluding stoppages the speed of bus is 60 km/hr and including stoppages it average speed becomes 48km/hr. For how much time the bus stops.
    a) 10 min
    b) 12 min
    c) 14 min
    d) 16 min
    e) None of these
    
    Answer & Explanation

    Answer – b) 12 min
    Explanation :
    Due to stoppages bus covers 12 km less. To cover 12km with 60km/hr speed it takes 12min
    

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