Two trains Ranipur Mail and Dhampur Mail start from Ranipur to Dhampu

Question

Two trains Ranipur Mail and Dhampur Mail start from Ranipur to Dhampur and from Dhampur to Ranipur respectively. After passing each other, they take 4 hours 48 minutes and 3 hours 20 minutes to reach Dhampur and Ranipur respectively. If Ranipur Mail is moving at 45 km/hr, the speed of Dhampur Mail is -

(A) 37.5 km/hr
(B) 54 km/hr
(C) 58 km/hr
(D) 60 km/hr
(E) 64.8 km/hr

Show Answer

Official Answer

B

(A) 37.5 km/hr
(B) 54 km/hr
(C) 58 km/hr
(D) 60 km/hr
(E) 64.8 km/hr

ashakank · Answer

RD t+4 hours 48 minutes = 4.8 Speed ->45km/h
DR t+3 hours 20 minutes = 3.34. Speed ->xkm/h

45t= 3.34b
bt=45*4.8 = 216

45t=3.34(216/t)

t=4

45 (t+4.8)=x(t+3.34)
45 (8.8)=x(7.34)

Around 54

JaiPavuluri · Answer

@bunel

This question takes longer to solve, is there a easy way out?

av1901 · Answer

Did take a while to figure out but once you do, you feel that it was simple enough to figure out sooner. Story of GMAT I guess

Anyways, question: Two trains Ranipur Mail and Dhampur Mail start from Ranipur to Dhampur and from Dhampur to Ranipur respectively. After passing each other, they take 4 hours 48 minutes and 3 hours 20 minutes to reach Dhampur and Ranipur respectively. If Ranipur Mail is moving at 45 km/hr, the speed of Dhampur Mail is -

So, we know that after passing each other, Ranipur Mail travels at 45kmph for 4.8hours so a distance of 216km.

Total Distance = (45*4.8) + (speed of dhampur*3.34) {Distance travelled by both from meeting point to destinations}

Now we know that they are both travelling to and from Ranipur and Dhampur, so let us see a diagram

Ranipur Mail (R ------> D) -----------------------Distance-------------------------------Dhampur Mail (R<---------- D)

-----------------RM/DM------------------------ (Meeting points)

After meeting point: ---------------RM ---------216km----------> Arrives Dhampur (45kmph for 4.8hours)

So that means that Dhampur Mail moving towards Ranipur travelled the same 216km to reach the point where they passed each other

Now that we have that cleared, we can say that at the time of meeting, Dhampur Mail travelled 216km and Ranipur Mail travelled 
Total-216km, and  we know that the time at which two meet is always same  so equation (Taking speed of Dhampur Mail as x)

T-216/45 = 216/x
10x/3*45 = 216/x
10x^2 = 3*45*216
10x^2 = 3*(3*3*5)*(2*2*2*3*3*3) : {Instead of multiplying and taking square root of big number, prime factorize so that easier to take square root}
To divide by 10, we just need to remove a 2 and a 5
So

x^2 = 2^2 * 3^6
x = 2 * 3^3 = 54

Answer - B

wickedvikram · Answer

Assume, trains meet at P, covering A&B distance respectively

(Tr1 @45km/h) R|<--------A----------->P<--------------B------------->|D(Tr2 @v km/h)
R|<--------(10/3 hrs by Tr2)----------->P<--------------(24/5 hrs by Tr1)------------->|D

We get 3 eqns from this question.
Since, time taken to reach P is same: A/45 = B/v ---- (1)

For Tr1:
B=24/5*45 ---- (2)

For Tr2:
A=10/3 * v ---- (3)

3 eqns & 3 variables, Solve it for v=54 km/h

Visssi · Answer

Apply formula Sa/Sb=√Tb/√Ta

Posted from my mobile device

faizan101 · Answer

Speed of Ranipur/speed of Dhampur =sqrt time taken by Dhampur/ time taken by Ranipur

45/d = √200/288
d= 45*12/10
d= 54

Two trains Ranipur Mail and Dhampur Mail start from Ranipur to Dhampu

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Two trains Ranipur Mail and Dhampur Mail start from Ranipur to Dhampu

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