Quantitative Aptitude: Time, Speed and Distance Set 21

1. Neelaksh is standing on a bridge which is 180 m long. He finds that a train crosses the bridge in 20 seconds but himself in 8 seconds. Find the speed of the train?
   54 kmph
   42 kmph
   45 kmph
   51 kmph
   None of these
   Option A
   A/8 =( A + 180) / 20 = 20A = 8(A + 180) = A = 120.
   Length of the train = 120 m.
   Speed of the train = [120/8]m/sec
   =[120/8] * 18/5kmph = 54 kmph.
   
    



2. Two express are running at 40 km/hr and 20 km/hr respectively in same direction. The fast express completely passes a women sitting in slower express in 5 seconds. What is the length of fast express?
   35
   27 (7/9)
   32(1/7)
   25
   None of these
   Option B
   Relative speed = (40-20) km/hr = [20 x 5/18] m/sec = [50/9] m/sec.
   Length of faster train=[50/9 x 5] m = 250/9 m
   
    



3. Excluding stoppages, the speed of a train is 54 kmph and including stoppages, it is 45 kmph. For how many minutes does the train stop per hour?
   15 minutes
   7 minutes
   12 minutes
   10 minutes
   None of these
   Option D
   Time taken to cover 9 km = (9/54 x 60) min = 10 minutes
   
    



4. A train starts with speed of 70 km/hr with its speed increasing every two hours by 10 kmph. In how many hours will it cover 345 kms?
   1 hours
   4.5 hours
   5 hours
   7.5 hours
   None of these
   Option B
   Distance covered in first 2 hours= (70 x 2) km
   Distance covered in next 2 hours= (80 x 2) km
   Remaining distance = 345 – (140 + 160) = 45 km.
   Speed in the 5th hour = 90 km/hr
   Time taken to cover 45 km = as speed is 90km/hr means it covers 90 km in 1 hour
   Total time taken = 2 + 2 +1/2=4 (1/2)hrs
   
    



5. Ramesh travelled from X to Y at a speed of 40 kmph and returns by increasing his speed by 50%. What is his average speed for both the trips?
   42 kmph
   48 kmph
   41 kmph
   40 kmph
   None of these
   Option B
   Average speed = [2 x 40 x 60] / [40 + 6]km/hr =4800/100km/hr =48 km/hr.
   
    



6. Three buses are running from a place P to another place Q. Their speeds are in the ratio of 4 : 3 : 5. The time ratio to reach Q by buses will be which of the following?
   15:20:12
   10:12:15
   16:18:20
   Cannot be determined
   None of these
   Option A
   Ratio of times taken [t=d/s or t indirectly proportional to s when distance is same]= (1/4) : (1/3) : (1/5) = 15 : 20 : 12
   
    



7. The distance between two states P and Q is 330 km. A bus starts from P at 8AM. and travels towards Q at 60 km/hr. Another bus starts from Q at 9AM. and travels towards P at 75 km/hr. At what time do they meet?
   11:15 AM
   11 AM
   10:30 AM
   10:15 AM
   None of these
   Option B
   Suppose they meet t hrs after 8AM
   Then,(Distance moved by first in t hrs) + [Distance moved by second in (t-1) hrs] = 330
   60t + 75(t–1) = 330 km
   t = 3
   So, they meet at (8 + 3), i.e. 11AM
   
    



8. Two buses of equal length are running on parallel lines in same direction at 46 km/hr and 36 km/hr. The faster bus passes the slower bus in 36 seconds. The length of each bus is which of the following?
   50
   45
   55
   60
   None of these
   Option A
   Relative speed= L/T
   (46-36) * 5/18 = [L + L ] / 36
   10 * (5/18) *36 * (1/2)= L
   L=50 m
   
    



9. A bus 125 m long passes a girl, running at 5 kmph in the same direction in which the bus is going, in 10 seconds. The speed of the bus is which of the following?
   45 kmph
   50 kmph
   40 kmph
   55 kmph
   None of these
   Option B
   
   
    



10. Two buses, one from Haldwani to Pune and the other from Pune to Haldwani, start simultaneously. After they meet, the buses reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is ?
    7:8
    3:5
    1:2
    4:3
    None of these
    Option D
    (P’s speed) : (Q’s speed) = square root of Q : square-root of P =square-root of 16 : square-root of 9 = 4 : 3