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Two cyclists left B for A simultaneously. The first cyclist stopped after 98 min, when he was 2 km short of A and the other one stopped after 123 min, when he was 3 km short of A. If the first cycled as many kilometres as the second, the first one would need 27 min less than the second. Find the distance between B and A. 
  • a)
    49
  • b)
    54
  • c)
    98
  • d)
    60
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Two cyclists left B for A simultaneously. The first cyclist stopped af...
Let distance between B and A be x km.
First cyclist covered (x - 2) km in 98 min.
Second cyclist covered (x - 3) km in 123 min.
First cyclist will take (123 - 27) i.e. 96 min to cover (x - 3) distance.
∴ This means first cyclist covers 1 km in 2 min.
∴ In 98 min, he will cover 49 km.
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Most Upvoted Answer
Two cyclists left B for A simultaneously. The first cyclist stopped af...
Let's assume the distance between B and A is 'd' km.

Given:
- The first cyclist stops after 98 minutes, when he is 2 km short of A.
- The second cyclist stops after 123 minutes, when he is 3 km short of A.
- If the first cyclist had cycled the same distance as the second cyclist, he would have needed 27 minutes less.

Let's calculate the speed of each cyclist:
- The first cyclist's speed = (d - 2) km / 98 min
- The second cyclist's speed = (d - 3) km / 123 min

To find the distance, we can equate the speeds of both cyclists:
(d - 2) / 98 = (d - 3) / 123

Cross-multiplying, we get:
123d - 246 = 98d - 294

Simplifying the equation, we get:
25d = 48
d = 48/25
d = 1.92 km

But we need to find the distance in whole numbers, so the distance between B and A is approximately 2 km.

Therefore, the correct answer is option A) 49 km.
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Two cyclists left B for A simultaneously. The first cyclist stopped after 98 min, when he was 2 km short of A and the other one stopped after 123 min, when he was 3 km short of A. If the first cycled as many kilometres as the second, the first one would need 27 min less than the second. Find the distance between B and A.a)49b)54c)98d)60Correct answer is option 'A'. Can you explain this answer?
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