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    A person reaches his destination 40 minutes late if his speed is 3 km/hr and reaches 30 minutes before time if his speed is 4 km/hr. What is the dista
    Question



    A person reaches his destination 40 minutes late if his speed is 3 km/hr and reaches 30 minutes before time if his speed is 4 km/hr. What is the distance of his destination from the starting point? (in km)

    A.

    12

    B.

    13

    C.

    10

    D.

    14

    Correct option is D

    Given:
    A person reaches his destination 40 minutes late if his speed is 3 km/hr and reaches 30 minutes before time if his speed is 4 km/hr.
    Let the distance be xx km.
    According to the question:
    - At 3 km/h → 40 minutes late
    - At 4 km/h → 30 minutes early
    Thus, the total time difference is:
    40+30=70 minutes=76 hours40 + 30 = 70 \text{ minutes} = \frac{7}{6} \text{ hours}
    Using the time formula: Time=DistanceSpeed\text{Time} = \frac{\text{Distance}}{\text{Speed}} 
    x3x4=76Taking LCM:4x3x12=76x12=76Cross-multiplying:x=76×12x=14Thus, the distance is:14 km\frac{x}{3} - \frac{x}{4} = \frac{7}{6} \\\text {Taking LCM}: \\\frac{4x - 3x}{12} = \frac{7}{6} \\\frac{x}{12} = \frac{7}{6} \\\text {Cross-multiplying}: \\x = \frac{7}{6} \times 12 \\x = 14 \\ \text {Thus, the distance is}: \\{14 \text{ km}}
    Correct answer is (d)
    ​​​​

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