Multiple choice

A boat takes (25 + N) hours for travelling downstream from point P to point Q and coming back to point R, which is M km from point Q. The distance between point P and point Q is D km. The boat takes 15 hours downward to cover distance from point P to point R, which is 75% of the distance from point P to point Q. The velocity of the stream is (4 - W) km/hr, the speed of the boat in still water is (14 + W) km/hr and the upstream speed of boat is 12 km/hr. Which of the following can be determined? A. Value of N B. Value of D C. Value of M D. Value of W

  1. All A, B, C and D

  2. Only B and C

  3. Only D and B

  4. Only A

  5. Only C
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A Correct answer
Explanation

The problem provides sufficient variables (N, D, M, W) and equations (downstream/upstream speeds, time taken, distances) to solve for all unknowns.

AI explanation

The upstream speed is given as 12 km/hr, which equals (14 + W) - (4 - W), so 18 + 2W = 12, making W = -3. Using W, the boat's speed in still water is 14 - 3 = 11 km/hr, and the stream's speed is 4 - (-3) = 7 km/hr. Since the boat travels from P to R downstream in 15 hours, the distance PR equals 15 times (11 + 7), which is 270 km. Because PR is 75% of D, the distance D equals 270 divided by 0.75, which is 360 km. The time taken to travel the full distance D downstream is 360 divided by 18, or 20 hours. Since the downstream journey from P to Q takes 20 hours and the upstream journey from Q to R takes 15 hours, the total time is 35 hours. The equation 25 + N = 35 gives N = 10. The distance M from Q to R is the difference between PQ and PR, calculated as 360 - 270 = 90 km. All four values can be determined.

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