Two persons X and Y start simultaneously from A and B and walk towards each…
2025
Two persons X and Y start simultaneously from A and B and walk towards each other. They meet after 1/2 hour and continue to walk towards their destination. If X reaches 25 minutes after Y reached the destination, find the ratio of their speeds.
- A.
3/7
- B.
⅔
- C.
5/9
- D.
11/18
Attempted by 17 students.
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Correct answer: B
Solution: Let the speeds of X and Y be x and y (units per hour).
They meet after 1/2 hour, so the distances they cover until meeting add to the total distance D:
x*(1/2) + y*(1/2) = D ⇒ D = (x + y)/2.
Total time for X to reach B = D/x. Total time for Y to reach A = D/y. Given X reaches 25 minutes (5/12 hour) after Y:
D/x = D/y + 5/12.
Let r = x/y. Take y = 1 and x = r. Then D = (r + 1)/2.
Substitute into the time equation: (r + 1)/(2r) = (r + 1)/2 + 5/12.
Simplify: (r + 1)/(2r) - (r + 1)/2 = 5/12 ⇒ (r + 1)(1/r - 1)/2 = 5/12.
Further simplification gives (r^2 - 1)/(2r) = -5/12 ⇒ 12(r^2 - 1) = -10r ⇒ 6r^2 + 5r - 6 = 0.
Solve the quadratic: r = [-5 ± 13]/12. The positive root is r = 8/12 = 2/3.
Therefore the speeds ratio x:y = 2:3, so x/y = 2/3.