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A deer and a rabbit can complete a full round on a circular track in 9 minutes and 5 minutes respectively. P, Q, R and S are the four consecutive points on the circular track which are equidistant from each other. P is opposite to R and Q is opposite to S. After how many minutes will they meet together for the first time at the starting point, when both have started simultaneously from the same point in same direction?
  • a)
    15 minutes
  • b)
    25 minutes
  • c)
    35 minutes
  • d)
    45 minutes
  • e)
    None of these
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
A deer and a rabbit can complete a full round on a circular track in 9...
Time taken by a deer to complete one round = 9 minutes
Time taken by a rabbit to complete one round = 5 minutes
They meet together for the first time at the starting point = LCM of 9 and 5 = 45 minutes.
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Most Upvoted Answer
A deer and a rabbit can complete a full round on a circular track in 9...
Problem Statement:
A deer and a rabbit can complete a full round on a circular track in 9 minutes and 5 minutes respectively. P, Q, R and S are the four consecutive points on the circular track which are equidistant from each other. P is opposite to R and Q is opposite to S. After how many minutes will they meet together for the first time at the starting point, when both have started simultaneously from the same point in the same direction?

Solution:

Let the total distance of the circular track be D.

Speed of deer = Distance traveled by deer/Time taken by deer = D/9

Speed of rabbit = Distance traveled by rabbit/Time taken by rabbit = D/5

Let both deer and rabbit start simultaneously from point P in the same direction.

When both the deer and the rabbit meet for the first time at the starting point, the distance traveled by the deer and rabbit respectively is equal to the distance around the circular track plus the distance between their starting points.

Distance traveled by the deer = Distance traveled by rabbit + Distance between their starting points

D + Distance between P and R = (D/9) * t

D + Distance between P and Q = (D/5) * t

Where t is the time taken for both deer and rabbit to meet for the first time at the starting point.

Distance between P and R = Distance between P and Q = D/2

Solving the above equations, we get t = 45 minutes.

Therefore, after 45 minutes, both deer and rabbit will meet together for the first time at the starting point.

Hence, the correct answer is option D.
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Community Answer
A deer and a rabbit can complete a full round on a circular track in 9...
Time taken by a deer to complete one round = 9 minutes
Time taken by a rabbit to complete one round = 5 minutes
They meet together for the first time at the starting point = LCM of 9 and 5 = 45 minutes.
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A deer and a rabbit can complete a full round on a circular track in 9 minutes and 5 minutes respectively. P, Q, R and S are the four consecutive points on the circular track which are equidistant from each other. P is opposite to R and Q is opposite to S. After how many minutes will they meet together for the first time at the starting point, when both have started simultaneously from the same point in same direction?a)15 minutesb)25 minutesc)35 minutesd)45 minutese)None of theseCorrect answer is option 'D'. Can you explain this answer?
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