Elitmus
Exam
Numerical Ability
Time Distance and Speed
There are two stations Rampur and Kanpur. Distance between them is 273KM. Ist Train starts from Rampur & Travel with the speed of 51KMPH at 1:00 PM and 2nd Train starts from Kanpur & Travel with the speed of 60KMPH at 2:00 PM. 2nd Train's Driver note the distance btw both train after every 1 Minute. Find the no. of times he will get the distance in whole number.
Options:
A) 13
B) 7
C) 5
D)30
Read Solution (Total 14)
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- At 2 PM: 1st train would have covered 51kms...and 2nd would have just started...
Therefore, at 2 PM
Distance between them: 273-51= 222 Kms
and relative speed: 51+60 = 111 Km/hr
Now after each minute, distance between them will decrease by: 111/60 kms or 37/20 kms
Hence, we need whole number, therefore, denominator 20 should get cancelled...
therefore, we will get whole number after every 20 minutes:
Like: 2.20, 2.40, 3.00, 3.20 and 3.40...TOTAL: 5 TIMES. (at 4 pm, train will meet so no need)
therefore, C) 5 is the answer - 10 years agoHelpfull: Yes(62) No(5)
- the answer is 7.
also, consider the case when t=0 and t=120 mins (t=120 mins wen the 2 trains meet, distance btwn dem is 0.) - 10 years agoHelpfull: Yes(15) No(3)
- 5
after every 20 mins, the distance will be decreased by 37 kms as
relative speed = 51+60=111 km/hr = 111/60 km/min= 37/20 km/min.
Trains will meet at 4.00 PM i.e. after 2 hr journey by train from kanpur.
so distance in integers ( KMS) will be at 2.20 PM, 02.40 PM, 03.00 PM, 03.20 PM and 03:40 PM. - 10 years agoHelpfull: Yes(7) No(4)
- since the 2nd train started at 2pm, till that time 1st train covers distance 51 kms
hence remaining distance is 273-51=222 kms
we know when two trains are in opposite directions their speed are added hence total relative speed is 60+51 = 111 kms/hr or 1.85 kms/min
now both trains will meet after time 222/111 = 2 hrs..or 120 min
now let distance traveled by both trains till x th minute = 1.85*x
now 222 - 1.85*x = should be a whole no
x=0,20,40,60,80,100,120 satisfies,
at 120th minute distance between them is 0(whole no.)
so the answer will be 7
- 10 years agoHelpfull: Yes(7) No(2)
- its (C) 7
Consider case for t=0 and t=120 also. - 10 years agoHelpfull: Yes(6) No(1)
- is 0 whole no?
- 10 years agoHelpfull: Yes(5) No(2)
- let train starts form Rampur at time x ,
51x+60(x-1)=273
111x=333
x=3h
now, 60/3 min =20 min
so at every 20 min(20*1 min) distance is noted i.e 60/20= 5 - 10 years agoHelpfull: Yes(5) No(3)
- 5 is the answer i guess
- 10 years agoHelpfull: Yes(3) No(7)
- Actually Option B was not there So the Correct Ans is 5.
- 10 years agoHelpfull: Yes(3) No(0)
- answr would be 7 b'coz 0 is a whole no.
and @ sharp 2 the distance is 222 which is a whole no.s and we will get other whole nums value of dist. at every 20 mints including @ 4:00.
B'coz 0 is a whole numb. - 9 years agoHelpfull: Yes(1) No(0)
- in 1 hr rampur train will cover 51 Km and after that kanpur train starts.
relative distance=273-51= 222 km
relative speed=51+60=111 km/h
in 1 min relative distance=111/60=37/20
to be whole no it should be multiple of 20 i.e after every 20 min it become whole no
2.20,2.40,3.00,3.20.3.40= 5 times - 8 years agoHelpfull: Yes(0) No(0)
- actually it is not given till what time the driver notes the distance between the trains...it might be after they meet and start going away from each other???
- 8 years agoHelpfull: Yes(0) No(0)
- let total distance of the pool is d.
case 1;
time taken by east diver-50/Se.
time taken by west diver for 1st meeting=(d-50)/Sw.
therefore for 1st meeting point-- 50/Se=(d-50)/Sw.
Se/Sw=50/(d-50)------------------------1
case 2;
time taken by east diver for 2nd meeting= (d-50+20)/Se
time taken by west diver for 2nd meeting= 100+(d-50-20)/Sw
therefore for 2nd meeting=Se/Sw=(d-30)/(d+50)---------2
from eqn 1 and 2 we get
(d-30)/(d+30)=50/(d-50)
solving we get
d=130.
this is the correct sol. - 8 years agoHelpfull: Yes(0) No(1)
- The distance travel by the 1st train (started at 1:00 PM) during 1st hour of its journey is 51km.
The second trains starts at 2:00PM and the distance between both the train at that moment is (273-51) = 222KM which must be noted by the driver.
They will meet in 2 hours i,e 4:00 PM (Train 1 will cover 102KM and Train 2 will cover 120KM).
Since the speed of train 2 is 60 KMPH i.e it will travel 1 KM in every 1 Min and for the distance between 2 trains to be a whole nos the minimum time interval which should be taken is 20 min in which train 1 will cover a distance of 17km. So after interval of every 20 min the distance will be a whole nos.
So the times are: 2;00PM, 2:20PM, 2;40PM, 3:00PM, 3;20PM, 3:40PM,4:00PM i.e 7 times.
Here 4:00PM is included because at 4:00PM the distance between them is '0' which is also a whole nos. - 7 years agoHelpfull: Yes(0) No(0)
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