Question Bank  100 CAT level questions on Time, Speed and Distance topic

Q91) A man completes a journey in 20 hours. He travels half of the journey’s distance at the rate of 84 km/hr and the other half of the journey’s distance at the rate of 96 km/hr. Find the total distance that the man covered during the journey?

Q92) Four people A, B, C, and D are running around a circular ground in a 432 km race of 2 laps. Initially they all are separated by 1/4th of the circumference of the ground and their speeds are 10 m/s, 20 m/s, 30 m/s and 40 m/s respectively. After every hour they all exchange their speeds such that A takes B's speed, B takes D's speed, C takes A's speed and D takes C's speed. Find the time taken by the winner to finish the race.

Q93) A railway track runs parallel to a road and a cyclist whose speed is 12kmph meets a trains at the crossing,same time everyday. One day cyclist started 25min late and met the train 6km ahead of the crossing. What is the speed of the train?
a. 60
b. 72
c. 90
d. 84

Q94) Rohan, Shikha’s boyfriend, had to pick her from her home for a live concert on her 23rd birthday. The venue of the concert and Shikha’s home were in opposite directions from Rohan’s office. He got late because of some work at office and realised that if he goes to pick Shikha from her home, which was a 48minute drive from his office, they would be late for the show by 16 minutes. He asked her to start from her home towards his office in an autorickshaw and himself started driving towards her home. Both of them started simultaneously, he picked her as soon as they met and they managed to reach the venue just in time for the concert. If Rohan drives at an average speed of 60 km/hr, find the speed (in km/hr) of the autorickshaw.

Q95) A starts from Bombay to Delhi. After a while he realizes he would cover 3/4 th of the distance in scheduled time and hence doubles his speed and reaches on time. He would have been late by 3 hours if he didn't change the speed. So after how much time from the start he changes the speed ?

Q96) Two motorists leave from opposite ends of a road at the same time and travel at constant but different speeds. They pass each other 700 meters from one end and continue to the other end of the road, where they turn around. On their return trip the motorists pass again—this time 400 meters from the opposite end of the road. How wide is the road?

Q97) Two guns were fired from the same place at an interval of 12min;but a person in the train approaching the place hears the second shot 10 min after the first. The speed of the train, if speed of sound is 330m/s

Q98) P and U stay next to each other and study in the same school. P and U start walking towards their school at the speed of 2km/hr and 3 km /hr respectively. The faster of the two reaches the school first and turns around and starts walking back. If P and U meet 200m away from the home, what is the distance between their residence and the school?
a) 260m
b) 240m
c) 200m
d) 250m

Q99) A bird is sitting on a train A moving at a Speed of 40 kmph. It sees another train B at a Distance of 200 ms with Speed of 60 kmph coming from the opposite direction on the same rail track. It flies with an average Speed of 10kmph and sits on another train. Again immediately it flies back to the first train and again to the second train and so on. It does so before the two trains crash. What is the total Distance traveled by the bird?

Q100) Rishi Kapoor can swim a certain course against the river flow in 84 minutes; he can swim the same course with the river flow in 9 minutes less than he can swim in still water. How long would he take to swim the course with the river flow?

total steps be T
T/N T/(N+4) =6
3N^2+12N2T=0 N=12+rt (144+24T) /6 (1)
and T/(G4)T/G = 6
3G^2 12G2T=0
G= 12+rt (144+24T) /6 (2)
relative speed = N+G
so T= 4N+4G (3)
using 1 and 2,
T = 4 * rt (144+24T)/3
9T^2 = 16 (144+24T)
9T^2  384T2304 = 0
T = (384 + 480)/18 = 48 steps

P's distance be Y, Q's be X
Y/50 = (X50)/25
Y=2X100
say Y=100, X=100
distance at any time=d
d^2 = (10050t)^2 + (10025t)^2
diff wrt t for minima
(10050t)*2 +(10025t) = 0
t=12/5
d^2 = 20^2 + 40^2 = 2000 so d= 20 rt 5

Train speed= T, men speed: v1, v2. length L.
so L/(Tv1)=20 and L/(T+v2) = 18
so 20T20v1=18T+18v2
T= 9v2+10v1 (1)
Ditsane between the men = 600 (T+v2)
Distance covered in these 10 mins = 600(v1+v2)
so reqd time = {600(T+v2)600(v1+v2)}/(v1+v2)
= (6000600)= 5400 sec= 90 mins ( using 1)

A=2x, B=x
length= 2pi*r = 49pi = 154 m.
so given, 154/3x = 14 x=11/3 so 2x=22/3

@mbatious answer 35?


@mbatious 9 hour 54 min is it?

@mbatious 6:24 am?

Let the distance between Home and School be D and the uniform speed during onward journey be S.
While coming back, 2D/7 was covered with a speed of 2S/7
Remaining distance = 5D/7 and 3/5th of this is 3D/7 which is covered with a speed of 3S/7.
He finally reduces the speed to 3S/7  12S/42 = S/7 (as 66.67% is equivalent to 2/3rd) and cover the remaining distance, 2D/7.Average speed for the total journey = 14 kmph
2D/14 = D/S + (2D/7) * (7/2S) + (3D/7) * (7/3S) + (2D/7) * (7/S)
D/7 = D/S + D/S + D/S + 2D/S
1/7 = 5/S
S = 35 kmph

@mbatious option d