Question

Trains A and B start traveling at the same time towards each other with constant speeds from stations X and Y, respectively. Train A reaches station Y in 10 minutes while train B takes 9 minutes to reach station X after meeting train A. Then the total time taken, in minutes, by train B to travel from station Y to station X is

• A. 15
• B. 12
• C. 6
• D. 10

Answer 1

Answer: (A)

15

Answer 2

Given:
Train A reaches station Y in 10 minutes.
Train B takes 9 minutes to reach station X after meeting train A.
Let's assume that the meeting point of the two trains between stations X and Y is M.
Time taken by train A to travel from X to M = t minutes
Time taken by train B to travel from Y to M = t minutes
Time taken by train A to travel from M to Y = (10 - t) minutes
Time taken by train B to travel from M to X = 9 minutes
Since the two trains start simultaneously and travel equal distances, we can use the ratio of time taken by them:
$\frac{t}{9}=\frac{(10 - t)} {t}$
Now, let's solve for 't':
$t^2 = 9(10 - t)$
$t^2 = 90 - 9t$
$t^2 + 9t - 90 = 0$
(t + 15)(t - 6) = 0
t = 6 (since time cannot be negative)
So, the time taken by train B to travel from station Y to station X is 6 + 9 = 15 minutes.
Hence, the correct answer is 15 minutes.