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jackfr2
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Two trains A and B start simultaneously in the opposite direction from 12 Apr 2020, 02:24
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46% (02:30) correct 54% (02:33) wrong based on 167 sessions

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Two trains A and B start simultaneously in the opposite direction from two points P and Q and arrive at their destinations(Q and P) 16 and 9 hours respectively after their meeting each other. At what speed does the second train B travel if the first train travels at 120 kmph

A. 90 kmph
B. 200 kmph
C. 240 kmph
D. 160 kmph
E. 360 kmph
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D
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Two trains A and B start simultaneously in the opposite direction from 12 Apr 2020, 05:04
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jackfr2
Two trains A and B start simultaneously in the opposite direction from two points P and Q and arrive at their destinations(Q and P) 16 and 9 hours respectively after their meeting each other. At what speed does the second train B travel if the first train travels at 120 kmph

A. 90 kmph
B. 200 kmph
C. 240 kmph
D. 160 kmph
E. 360 kmph

\(S_A/S_B = √(t_B/t_A)\)

\(120/S_B = √(9/16)\)

\(S_B = 160\)

Answer: Option D
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Two trains A and B start simultaneously in the opposite direction from 12 Apr 2020, 03:29
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Distance covered by train A till both trains meet =\( L_A\)
Distance covered by train B till both trains meet =\( L_B\)

Speed of train A = \(V_A\)
Speed of train B = \(V_B\)


\(\frac{L_A}{v_A}\) = \(\frac{L_B}{v_B}\)

\(\frac{L_A}{L_B}\) = \(\frac{v_A}{v_B}\).......(1)

Given-
\(\frac{L_A}{v_B} = 9\).....(2)

\(\frac{L_B}{v_A} = 16\)....(3)

Divide (2) by (3)
\(\frac{L_A}{L_B} *\frac{v_A}{v_B} =\frac{ 9}{16}\)

\((\frac{v_A}{v_B})^2 = (\frac{3}{4})^2\)

\(\frac{v_A}{v_B}= \frac{3}{4}\)

\(\frac{120}{v_B} = \frac{3}{4}\)

\(v_B = 160\)



jackfr2
Two trains A and B start simultaneously in the opposite direction from two points P and Q and arrive at their destinations(Q and P) 16 and 9 hours respectively after their meeting each other. At what speed does the second train B travel if the first train travels at 120 kmph

A. 90 kmph
B. 200 kmph
C. 240 kmph
D. 160 kmph
E. 360 kmph
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Two trains A and B start simultaneously in the opposite direction from 27 May 2020, 00:13
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The basic things to understand here are:
1) Since the two trains start together, they must have travelled for the same time period till they meet at a point.
2) the distance travelled by A before they met = distance travelled by B after they met.
The distance travelled by A after they met = distance travelled by B before they met.
Let the time for which they both travelled before they met be t1.

:1) Sa.16 = Sb.t1 and 2) Sa.t1= Sb.9
Dividing equation 1) with equation 2) :
16/t1 = t1/9 ; t1= 12 hrs.
Put t1=12 in any equation.

We get Sb= 160

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Two trains A and B start simultaneously in the opposite direction from 08 Mar 2025, 07:26
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What's this method/formula called?
GMATinsight
jackfr2
Two trains A and B start simultaneously in the opposite direction from two points P and Q and arrive at their destinations(Q and P) 16 and 9 hours respectively after their meeting each other. At what speed does the second train B travel if the first train travels at 120 kmph

A. 90 kmph
B. 200 kmph
C. 240 kmph
D. 160 kmph
E. 360 kmph

\(S_A/S_B = √(t_B/t_A)\)

\(120/S_B = √(9/16)\)

\(S_B = 160\)

Answer: Option D
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Two trains A and B start simultaneously in the opposite direction from 08 Mar 2025, 07:55
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Divyanshu14
What's this method/formula called?
GMATinsight
jackfr2
Two trains A and B start simultaneously in the opposite direction from two points P and Q and arrive at their destinations(Q and P) 16 and 9 hours respectively after their meeting each other. At what speed does the second train B travel if the first train travels at 120 kmph

A. 90 kmph
B. 200 kmph
C. 240 kmph
D. 160 kmph
E. 360 kmph

\(S_A/S_B = √(t_B/t_A)\)

\(120/S_B = √(9/16)\)

\(S_B = 160\)

Answer: Option D
I'm not sure if this formula has a name to it, but whenever two entities starting from opposite ends at the same time meet at a common point and the total distance they travelled is D, the ratio of their speeds \(\frac{Sa}{Sb} = \sqrt{\frac{Tb}{Ta}}\), where Tb and Ta is the time taken to reach their destination from the common point.

Here's another application of the same formula on a different question, along with a detailed answer / derivation: https://gmatclub.com/forum/a-and-b-are- ... l#p3463553
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