Here is the extracted text:
"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) 6
b) 15
c) 10
d) 12"
The question involves two trains, A and B, which are traveling toward each other, with given speeds and times to reach their respective stations after meeting.
From the documents, we note that:
1. Train A reaches station Y in 10 minutes.
2. After meeting Train A, Train B takes 9 minutes to reach station X.
To determine the time taken by Train B to travel from station Y to station X after they meet, we apply the concept of relative speed and the proportionality based on the time taken by each train to reach its destination after meeting.
Given that:
- Time taken by Train A after meeting Train B = 10 minutes
- Time taken by Train B after meeting Train A = 9 minutes
Using the ratio of their respective times to estimate the distance or speed comparison, we find:
- The ratio of speed can be derived from the square roots of the time ratios as \( SA/SB = (TB)^{1/2} / (TA)^{1/2} \).
Since we have established that:
- The time intervals are (10 and 9), hence the speed ratio indicates that for every 10 units of distance Train A travels, Train B travels 9 units.
To find out the total time taken by Train B from station Y to X after they meet:
- The options provided for total time taken by Train B to reach station X from Y are: 6, 15, 10, and 12 minutes.
Given the context, the total time that corresponds correctly to the calculation and ratio found from proportionality is 6 minutes for Train B after meeting Train A to reach its destination.
Therefore, the answer is:
6 minutes.
(Explanation derived from the gathered information on speed and time ratios pertinent to the traveling time between trains.)
