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    Question

    A boat can cover ‘y’ km distance downstream in

    (t+2.5) hours. The same boat can cover ‘0.25y’ km distance upstream in ‘t’ hours. The time taken by the boat to cover 728 km in still water is (2t+3) hours. If the total time taken by the boat to cover ‘y’ km distance downstream and the same distance upstream is 65 hours, then find out the speed of the stream.
    A 16 km/h Correct Answer Incorrect Answer
    B 24 km/h Correct Answer Incorrect Answer
    C 12 km/h Correct Answer Incorrect Answer
    D 20 km/h Correct Answer Incorrect Answer
    E None of the above Correct Answer Incorrect Answer

    Solution

    Let’s assume the speed of the boat in still water and the speed of the stream are ‘B’ and ‘C’ respectively.

    A boat can cover ‘y’ km distance downstream in (t+2.5) hours.

    (B+C) = y/(t+2.5)

    y/(B+C) = (t+2.5)    Eq.(i)

    The same boat can cover ‘0.25y’ km distance upstream in ‘t’ hours.

    (B-C) = 0.25y/t

    0.25y/(B-C) = t

    y/[4(B-C)] = t

    y/(B-C) = 4t    Eq.(ii)

    If the total time taken by the boat to cover ‘y’ km distance downstream and the same distance upstream is 65 hours.

    (y/(B+C))+(y/(B-C)) = 65

    Put Eq.(i) and Eq.(ii) in the above equation.

    (t+2.5)+4t = 65

    5t+2.5 = 65

    5t = 65-2.5

    5t = 62.5

    t = 12.5    Eq.(iii)

    The time taken by the boat to cover 728 km in still water is (2t+3) hours.

    728/B = (2t+3)

    Put the value of ‘t’ from Eq.(iii) in the above equation.

    728/B = (2x12.5+3)

    728/B = (25+3)

    728/B = 28

    728/28 = B

    B = 26    Eq.(iv)

    Put the value of ‘B’ and ‘t’ in Eq.(i) and Eq.(ii).

    y/(26+C) = (12.5+2.5)

    y = 15(26+C)    Eq.(v)

    y/(26-C) = 4x12.5

    y/(26-C) = 50

    y = 50(26-C)    Eq.(vi)

    Equating Eq.(v) Eq.(vi).

    15(26+C) = 50(26-C)

    3(26+C) = 10(26-C)

    78+3C = 260-10C

    13C = 260-78

    13C = 182

    C = 14

    So the speed of the stream = 14 km/h

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