πŸ“’ Too many exams? Don’t know which one suits you best? Book Your Free Expert πŸ‘‰ call Now!


    Question

    The speed of the boat in still water is β€˜y’ % more

    than the speed of the boat in upstream. The time taken by the boat to cover (2d+50) km distance in downstream is 3.5 hours less than the time taken by the same boat to cover β€˜d’ km distance in upstream. The same boat can cover (d+75) km distance in still water in (y/6) hours. If the speed of stream is 30 km/h, then which of the following statements is/are true? (i) The value of β€˜y’ is the multiple of 5. (ii) The speed of boat in still water should not be more than 60 km/h. (iii) The value of β€˜d’ is a four digit number.
    A Only (i) Correct Answer Incorrect Answer
    B Only (ii) Correct Answer Incorrect Answer
    C Only (iii) Correct Answer Incorrect Answer
    D Only (ii) and (iii) Correct Answer Incorrect Answer
    E Only (i) and (iii) Correct Answer Incorrect Answer

    Solution

    Let’s assume the speed of boat in still water and the speed of stream are β€˜B’ and β€˜C’ respectively. If the speed of stream is 30 km/h. C = 30 km/h The speed of the boat in still water is β€˜y’ % more than the speed of the boat in upstream. B = (100+y)% of (B-C) Put the value of β€˜C’ in the above equation. B = (100+y)% of (B-30) 100B = (100+y)x(B-30) [100B/(B-30)] = (100+y) y = [100B/(B-30)] - 100Β  Β  Eq.(i) The time taken by the boat to cover (2d+50) km distance in downstream is 3.5 hours less than the time taken by the same boat to cover β€˜d’ km distance in upstream. [(2d+50)/(B+C)] = [d/(B-C)] - 3.5 Put the value of β€˜C’ in the above equation. [(2d+50)/(B+30)] = [d/(B-30)] - 3.5 [d/(B-30)] - [(2d+50)/(B+30)] = 3.5Β  Β  Eq.(ii) The same boat can cover (d+75) km distance in still water in (y/6) hours. (d+75)/B = (y/6) Put the value of β€˜y’ from Eq.(i) in the above equation. (d+75)/B = [[100B/(B-30)] - 100]/6 (d+75) = B[[100B/(B-30)] - 100]/6 d = B[[100B/(B-30)] - 100]/6 - 75Β  Β  Eq.(iii) Put the value of β€˜d’ from Eq.(iii) to Eq.(ii). [[B[[100B/(B-30)] - 100]/6 - 75]/(B-30)] - [(2x[B[[100B/(B-30)] - 100]/6 - 75]+50)/(B+30)] = 3.5 After solving the above equation, there will be three values of β€˜B’. But two of them will be negative. So these can be eliminated. Hence B = 70 which is the only possible value. Put the value of β€˜B’ in Eq.(i). y = [100x70/(70-30)] - 100 y = [7000/40] - 100 y = 175 - 100 y = 75 Put the value of β€˜B’ in Eq.(ii). [d/(70-30)] - [(2d+50)/(70+30)] = 3.5 [d/40] - [(2d+50)/100] = 3.5 [d/40] - [(d+25)/50] = 3.5 [5d/200] - [4(d+25)/200] = 3.5 5d - 4d - 100 = 3.5x200 d - 100 = 700 d = 700+100 d = 800 (i) The value of β€˜y’ is the multiple of 5. The above given statement is true. (ii) The speed of boat in still water should not be more than 60 km/h. The above given statement is not true. (iii) The value of β€˜d’ is a four digit number. The above given statement is not true.

    Practice Next

    Relevant for Exams:

    ask-question

    Not sure which exam is best for you Talk to our expert

    Get My Free Call