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    Question

    Two friends K and L are at points R and S respectively.

    K heads from R toward S at a speed of (x – 4) km/h. After 2 hours, L starts from S toward R at (x + 4) km/h. They meet exactly at the midpoint of RS. If RS = 234 km, find the total time taken by K to go from R to S.
    A 18 hrs Correct Answer Incorrect Answer
    B 20 hrs Correct Answer Incorrect Answer
    C 13 hrs Correct Answer Incorrect Answer
    D 24 hrs Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    ATQ, Distance covered by K in 2 hours = (x – 4) × 2 = 2(x – 4) km Remaining distance = 234 – 2(x – 4) = 234 – 2x + 8 = (242 – 2x) km Time of meet after L starts = (242 – 2x)/(2x) hours According to question, [(242 – 2x)/(2x)] × (x + 4) = 234/2 ⇒ –2x² + 968 = 0 ⇒ 2x² = 968 ⇒ x² = 484 ⇒ x = 22 Speed of K = x – 4 = 22 – 4 = 18 km/h Therefore, required time = 234/18 = 13 hours

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