DIRECTIONS: Choose the most appropriate answer.Q. The speed of a boat in still water is 10 Kmph. If it can travel 26 Km downstream and 14 Km upstream in the same time, the speed of the stream isa)2 Kmphb)2.5 Kmphc)3 Kmphd)4 KmphCorrect answer is option 'C'. Can you explain this answer?

Question

Answer

Problem Analysis:
Let's assume the speed of the stream is 'x' kmph.
The speed of the boat in downstream (boat moving along the stream) would be the sum of the speed of the boat in still water and the speed of the stream, i.e., 10 + x kmph.
Similarly, the speed of the boat in upstream (boat moving against the stream) would be the difference between the speed of the boat in still water and the speed of the stream, i.e., 10 - x kmph.

Given Information:
Speed of the boat in still water = 10 kmph
Distance downstream = 26 km
Distance upstream = 14 km
Time taken for downstream and upstream travel is the same.

Solution:
Let's calculate the time taken for downstream and upstream travel using the given information and the formula: Time = Distance/Speed.

Downstream:
Distance downstream = 26 km
Speed downstream = 10 + x kmph
Time taken downstream = Distance downstream / Speed downstream = 26 / (10 + x) hours

Upstream:
Distance upstream = 14 km
Speed upstream = 10 - x kmph
Time taken upstream = Distance upstream / Speed upstream = 14 / (10 - x) hours

Since the time taken for downstream and upstream travel is the same, we can equate the two expressions for time:

26 / (10 + x) = 14 / (10 - x)

Solving the equation:
To solve this equation, we can cross-multiply and simplify:

26(10 - x) = 14(10 + x)
260 - 26x = 140 + 14x
40x = 120
x = 3

Therefore, the speed of the stream is 3 kmph. Hence, the correct answer is option C, 3 kmph.

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