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A truck travelled from town A to town B over several days. During the first day, it covered 1/p of the total distance, where p is a natural number. During the second day, it travelled 1/q of the remaining distance, where q is a natural number. During the third day, it travelled 1/P of the distance remaining after the second day, and during the fourth day, 1/q of the distance remaining after the third day. By the end of the fourth day the truck had travelled 3/4 of the distance between A and B.
If the total distance is 100 kilometers, the minimum distance that can be covered on day 1 is kilometres.
  • a)
    25
  • b)
    30
  • c)
    33
  • d)
    35
  • e)
    40
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
A truck travelled from town A to town B over several days. During the...
Total distance = 100 km
Distance travelled on first day will be minimum when p is maximum i.e. p = 4
Hence, distance travelled on first day = 100/4= 25 km
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Most Upvoted Answer
A truck travelled from town A to town B over several days. During the...
To find the minimum distance that can be covered on day 1, let's consider the scenario step by step.

First Day:
- Let's assume the distance covered on the first day is x km.
- According to the given information, the truck covered 1/p of the total distance on the first day.
- So, 1/p * 100 = x
- Therefore, x = 100/p km

Second Day:
- On the second day, the truck covers 1/q of the remaining distance after the first day.
- The remaining distance after the first day is (100 - x) km.
- So, 1/q * (100 - x) = (100 - x)/q km

Third Day:
- On the third day, the truck covers 1/P of the distance remaining after the second day.
- The distance remaining after the second day is (100 - x)/q km.
- So, 1/P * (100 - x)/q = (100 - x)/qP km

Fourth Day:
- On the fourth day, the truck covers 1/q of the distance remaining after the third day.
- The distance remaining after the third day is (100 - x)/qP km.
- So, 1/q * (100 - x)/qP = (100 - x)/q^2P km

By the end of the fourth day, the truck had traveled 3/4 of the distance between A and B:
- The total distance is 100 km.
- So, the distance covered in the first four days is 3/4 * 100 = 75 km.
- The distance covered on the first day is x km, and the remaining distance covered in the next three days is (100 - x)/q^2P km.
- Therefore, x + (100 - x)/q^2P = 75 km

To find the minimum distance that can be covered on day 1, we need to minimize the value of x.
- Since x = 100/p km, we need to minimize the value of p.
- The minimum value of p is 4 (as the question states that p is a natural number).
- Therefore, the minimum distance that can be covered on day 1 is 100/4 = 25 km.

Hence, the correct answer is option A) 25.
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A truck travelled from town A to town B over several days. During the first day, it covered 1/p of the total distance, where p is a natural number. During the second day, it travelled 1/q of the remaining distance, where q is a natural number. During the third day, it travelled 1/P of the distance remaining after the second day, and during the fourth day, 1/q of the distance remaining after the third day. By the end of the fourth day the truck had travelled 3/4 of the distance between A and B.If the total distance is 100 kilometers, the minimum distance that can be covered on day 1 is kilometres.a) 25b) 30c) 33d) 35e) 40Correct answer is option 'A'. Can you explain this answer?
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A truck travelled from town A to town B over several days. During the first day, it covered 1/p of the total distance, where p is a natural number. During the second day, it travelled 1/q of the remaining distance, where q is a natural number. During the third day, it travelled 1/P of the distance remaining after the second day, and during the fourth day, 1/q of the distance remaining after the third day. By the end of the fourth day the truck had travelled 3/4 of the distance between A and B.If the total distance is 100 kilometers, the minimum distance that can be covered on day 1 is kilometres.a) 25b) 30c) 33d) 35e) 40Correct answer is option 'A'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A truck travelled from town A to town B over several days. During the first day, it covered 1/p of the total distance, where p is a natural number. During the second day, it travelled 1/q of the remaining distance, where q is a natural number. During the third day, it travelled 1/P of the distance remaining after the second day, and during the fourth day, 1/q of the distance remaining after the third day. By the end of the fourth day the truck had travelled 3/4 of the distance between A and B.If the total distance is 100 kilometers, the minimum distance that can be covered on day 1 is kilometres.a) 25b) 30c) 33d) 35e) 40Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A truck travelled from town A to town B over several days. During the first day, it covered 1/p of the total distance, where p is a natural number. During the second day, it travelled 1/q of the remaining distance, where q is a natural number. During the third day, it travelled 1/P of the distance remaining after the second day, and during the fourth day, 1/q of the distance remaining after the third day. By the end of the fourth day the truck had travelled 3/4 of the distance between A and B.If the total distance is 100 kilometers, the minimum distance that can be covered on day 1 is kilometres.a) 25b) 30c) 33d) 35e) 40Correct answer is option 'A'. Can you explain this answer?.
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