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    Question

    A man travels a specific distance at a given speed,

    completing the journey in a set amount of time. If he had reduced his speed by 10 km/h, it would have taken him an additional 2 hours to cover the same distance. Further, if he had decreased his speed by another 10 km/h (a total reduction of 20 km/h from the original speed), the journey would have taken an additional 3 hours beyond the initial 2-hour delay. Determine the total distance he traveled.
    A 400 km Correct Answer Incorrect Answer
    B 600 km Correct Answer Incorrect Answer
    C 750 km Correct Answer Incorrect Answer
    D 800 km Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    Let, distance be тАШdтАЩ km So, d/(s тАУ 10) тАУ d/s = 2 Or, 10d = 2s(s тАУ 10) Or, d = 2 ├Ч s(s тАУ 10)/10 -----(i) And, d/(s тАУ 20) тАУ d/s = 5 Or, 20d = 5 ├Ч s(s тАУ 20) Or, d = 5 ├Ч s(s тАУ 20)/20 --------(ii) From (i) and (ii), Let S1 = 10 km/h S2 = 20 km/h T1 = 2 hours T2 = 5 hours Let original speed be S km/h [(S тАУ 10) ├Ч 2]/10 = [(S тАУ 20) ├Ч 5]/20 4(S тАУ 10) = 5(S тАУ 20) 4S тАУ 40 = 5S тАУ 100 S = 60 km/h Required distance = 60 ├Ч (60 тАУ 10)/10 ├Ч 2 = 60 ├Ч 5 ├Ч 2 = 600 km

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