Aptitude - Problems on Trains - Discussion

Its an simple formula nd you all are making it so much complicated.

For this question the direct formulas are:
(A's speed) : (B's speed) = root(b) : root(a)
Time at which they meet= root(a*b)

Derivation to the formulas:

Let X be the total distance, t be the time at which they meet
a,b are times at which they reach the destination after they meet.
s1, s2 are speeds of train1, train2 respectively.

then X = t(s1+s2) ...(1)
X = (t+a)s1 ...(2)
X = (t+b)s2 ...(3)

after equating (1) and (2)
t.s2 = a.s1 ...(4)
after equating (1) and (3)
t.s1 = b.s2 ...(5)

multiply (4) and (5)
t.t.a.b = s1.s2.a.b

" t = root(a*b) "

substitute t value in either (4) or (5)

then " s1/s2 = root(b)/root(a) "

Its ok the formula is working but can anyone proove that formula!

A train travelled from Delhi to Patna and back in a certain time at the rate of 60kmph. But if the train had travelled from Delhi to Patna at rate of rate 80Kmph. And back from Patna to Delhi at the rate of 40Kmph. It would take two hours Longer. Find the distance between Delhi and Patna?

Detailed solution please.

L.C.M of 60,80 and 40 is 240..
so let be 240 is the distace .
then train with 60kmh will take 8 hrs to complete.
and trains with 80 kmh and 40 kmh will take 9 hrs to complete.

so the time difference is (9-8) =1.. so what is required is 4 hrs lap.

so multiply with 4 we will get 240*4 = 960 km ..that is the answer.

If distance between delhi and patna is x then, time taken in two conditions are :

1. 2x/60 and x/80+x/40
as eq. x/80+x/40= 2x/60+2

Simplified x=480.

Ishita Narula is correct

d1/d2=x1/x2;
d1=16x1;
d2=9x2;
9/16=(x1)2/(x2)2;
x1/x2=3/4;

Good job @ ISHITHA NARULA

I understand what you did there abhishek. There is just one Problem. The distance "X" which you are taking for both trains, how do you know it is the same. i.e. They are both travelling at different speeds, so they definitely won't meet at a mid point so there cannot be a single X for both train's distances, right?