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Two men A and B walk from P to Q, a distance of 21 km, at 3 and 4 km an hour respectively. B reaches Q, returns immediately and meets A at R. The distance from P to R is
- a)12 km
- b)18 km
- c)10 km
- d)24 km
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
Two men A and B walk from P to Q, a distance of 21 km, at 3 and 4 km a...
When B meets A at R, B has walked the distance PQ + QR and A the distance PR.
That is, both of them have together walked twice the distance from P to Q, i.e. 42 km.
Now, the speed of A and B are in the ratio 3 : 4, and they have walked 42 km.
Hence, the distance PR travelled by A = 3/7 of 42 km = 18 km.
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Community Answer
Two men A and B walk from P to Q, a distance of 21 km, at 3 and 4 km a...
Solution:
Let's break down the problem step by step:
1. Time taken by A and B to reach Q:
- Speed of A = 3 km/hr
- Speed of B = 4 km/hr
- Distance = 21 km
- Time taken by A = Distance/Speed = 21/3 = 7 hours
- Time taken by B = Distance/Speed = 21/4 = 5.25 hours
2. Meeting point R:
- When B reaches Q, he immediately returns towards P.
- By the time B reaches R, A would have covered a distance of 21 km.
- Since B takes 5.25 hours to reach Q and back, A covers 3 km/hr x 5.25 hrs = 15.75 km by the time they meet at R.
- Remaining distance from R to Q covered by B = 21 - 15.75 = 5.25 km
3. Calculating distance from P to R:
- Total distance from P to Q = 21 km
- Distance covered by A when B reaches Q = 21 km
- Distance covered by B from Q to R = 5.25 km
- Therefore, distance from P to R = 21 - 5.25 = 15.75 km
Hence, the distance from P to R is 15.75 km, which is closest to option B (18 km).
Let's break down the problem step by step:
1. Time taken by A and B to reach Q:
- Speed of A = 3 km/hr
- Speed of B = 4 km/hr
- Distance = 21 km
- Time taken by A = Distance/Speed = 21/3 = 7 hours
- Time taken by B = Distance/Speed = 21/4 = 5.25 hours
2. Meeting point R:
- When B reaches Q, he immediately returns towards P.
- By the time B reaches R, A would have covered a distance of 21 km.
- Since B takes 5.25 hours to reach Q and back, A covers 3 km/hr x 5.25 hrs = 15.75 km by the time they meet at R.
- Remaining distance from R to Q covered by B = 21 - 15.75 = 5.25 km
3. Calculating distance from P to R:
- Total distance from P to Q = 21 km
- Distance covered by A when B reaches Q = 21 km
- Distance covered by B from Q to R = 5.25 km
- Therefore, distance from P to R = 21 - 5.25 = 15.75 km
Hence, the distance from P to R is 15.75 km, which is closest to option B (18 km).
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