- Question
A train 110 metres long is running at a speed of 60 kmph. In how many seconds will it pass a lady who is running at a speed of 6 kmph in the direction opposite to that in which the train is going?
a)8
b)24
c)6
d)12
e)10
Explanation
SOLUTION[C]-
Speed of train relative to man = (60 + 6) km/hr = 66 km/hr.
[66*(5/18)] m/sec = (55/3) m/sec
Time taken to pass the man = [110*(3/55)]m/sec = 6 sec.
Question-2
Two trains are moving in opposite directions @ 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is:
a)50
b)46
c)45
d)49
e)48
Explanation
SOLUTION[E]
Relative speed =(60+90)km/hr=150km/hr=150×518m/sec=1253m/sec
Distance covered by the slower train to cross the faster train =(1.1+0.9)km=2km=2000m
The time taken by the slower train to cross the faster train in second =distancespeed=20001253=16×3=48 seconds
Question-3
A car of length 4m wants to overtake a trailer truck of length 20m travelling at 36 km/hr within 10 seconds. At what speed should the car travel?
a)12m/s
b)11.6m/s
c)10.6m/s
d)12.4m/s
e)14.8m/s
Explanation
SOLUTION[D]-
Car of length = 4m
Length of truck = 20m
Speed of truck = 36km / h * r
Formula used:-
(1) Both the car and the truck are traveling in the same direction relati = (S_{1} – S_{2})
(2) Speed (s) = Distance(d) / Time (t)
Calculation:-
Total distance to be covered by the car ‘ d’ = 20 + 4 = 24m
Let the speed of the car be = S_{1}*m / s
Speed of truck S_{2} = 36km / h * r = 10m / s
Speed of truck S_{2} = 36km / h * r = 10m / s
Both the car and the truck are traveling in the same direction and
we know that to overtake the truck, the speed of the car should be more than that of the truck
Relative speed = (S_{1} – S_{2}) , Time = 10s
⇒ Speed (s) = Distance(d) / Time (t)
Rightarrow (S_{1} – S_{2}) = d / t
(S1-10) = 24/10 S₁= 12.4 m/s 1
.: The required answer is 12.4
Question-4
A and B stand at distinct points of a circular race track of length 120m. They run at speeds of a m/s and b m/s respectively. They meet for the first time 16 seconds after they start the race and for the second time 40 seconds from the time they start the race. Now, if B had started in the opposite direction to the one he had originally started, they would have met for the first time after 40 seconds. If B is quicker than A, find B’s speed:
a)10 m/s
b)5 m/s
c)3 m/s
d)4 m/s
e)6 m/s
Explanation
SOLUTION[C]
Question-5
Due to some technical problem in the machine of his motorbike, Arojeeth had to decrease the speed to 75% of the normal speed and hence he was late for work by 2 hrs. What is the normal time taken by him to reach for his work at the normal speed ?
a)512 min
b)360 min
c)480 min
d)560min
e)240 min
Explanation
SOLUTION[C]-480
Question-6
Four friends, Ananyaa, Brian, Chaitra, and Deepali, decide to jog for 30 minutes inside a stadium with a circular running track that is 200 metres long. The friends run at different speeds. Ananyaa completes a lap exactly every 60 seconds. Likewise, Brian, Chaitra and Deepali complete a lap exactly every 1 minute 30 seconds, 40 seconds and 1 minute 20 seconds respectively. The friends begin together at the start line exactly at 4 p.m. What is
the total of the numbers of laps the friends would have completed
when they next cross the start line together?
a)43
b)37
c)47
d)26
e)46
Explanation
SOLUTION[47]C
All the four friends will meet at the starting point after LCM(60,90,40,80) = 720 seconds.
Number of laps by A in 720 seconds = 12
Number of laps by B in 720 seconds = 8
Number of laps by C in 720 seconds = 18
Number of laps by D in 720 seconds = 9
Together they complete = 47 laps
Question-7
A deer and a tiger are joyfully playing with each other. The deer notices that it is 40 steps away from the tiger and starts running towards it. At the same time, the tiger starts running away from the deer. Both run on the same straight line. For every five steps the deer takes, the tiger takes six steps. However, the deer takes only two steps to cover the distance that the tiger covers in three steps. In how many steps can the deer catch the tiger?
a)200
b)230
c)120
d)180
e)320
Explanation
SOLUTION[A]-
Let speed of deer = 5steps/second and speed of tiger = 6 steps/sec
Let deer cover 1 m in a step => tiger covers 2/3 m in a step
Hence speed of deer = 5m / s and spped of tiger = 6 * 2 / 3 * m / s = 4m / s
Hence time taken by a deer to catch tiger = 40 seconds
Distance travelled by deer in 40 seconds = 5 * 40 = 200 steps
Question-8
A 270 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train in metres ?
a)248
b)240
c)320
d)230
e)224
Explanation
SOLUTION[D] 230
Relative speed = (120 + 80) kmph =(200×5) m/sec =(509m/sec.
Let the length of the other train be ‘ x’ metres.
Then, (x + 270)/9 = 500 9 ⇔x+270=500 ⇔ x=230.
Question-9
A wheel makes 1000 revolutions in covering a distance of 88 kilometres. Find the radius of the wheel?
a)14 m
b)10 m
c)14.8 m
d)12.8 m
e)12 m
Explanation
SOLUTION[A]-14M
