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    Question

    P and Q each had designated spots

    to set up their temporary shops. The distance from their house (they live in the same house) to Pโ€™s shop was 32 km, and to Qโ€™s shop was 40 km. They usually left home at the same time and arrived at their respective shops by 8:00 a.m. One day, their shop locations were swapped. On that day, P left home 16 minutes earlier than Q so that he could reach his new spot on time. Find Pโ€™s speed.
    A 74 km/h Correct Answer Incorrect Answer
    B 54 km/h Correct Answer Incorrect Answer
    C 45 km/h Correct Answer Incorrect Answer
    D 84 km/h Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    ATQ,

    P and Q travel distances of 32 km and 40 km respectively. They both reach their destinations at the same time. Thus, their speed ratio is 32:40, which simplifies to 4:5. Assume Pโ€™s speed is 4x km/h and Qโ€™s speed is 5x km/h. On the interchange day: Time taken by P to travel to Qโ€™s place = 40 / (4x) hours Time taken by Q to travel to Pโ€™s place = 32 / (5x) hours According to the question: (40 / 4x) โ€“ (32 / 5x) = 16/60 Solving gives x = 13.5. Therefore, Pโ€™s speed = 4x = 54 km/h.

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