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Bouncing Marble Total Distance

XAT 2022 · Quantitative Ability & Data Interpretation · Medium · Progression

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A marble is dropped from a height of 3 metres onto the ground. After hitting the ground, it bounces and reaches 80%80\% of the height from which it was dropped. This repeats multiple times. Each time it bounces, the marble reaches 80%80\% of the height previously reached. Eventually, the marble comes to rest on the ground.

What is the maximum distance that the marble travels from the time it was dropped until it comes to rest?

  1. A.

    15 m

  2. B.

    27 m

  3. C.

    24 m

  4. D.

    12 m

  5. E.

    30 m

Answer

B

Explanation

Initial drop = 3 m3\text{ m}. Subsequent upward and downward journeys form infinite GP: Total Distance = 3+2×(3×0.8+3×0.82+… )3 + 2 \times \left(3 \times 0.8 + 3 \times 0.8^2 + \dots\right) =3+2×(2.41−0.8)=3+2×12=27 m= 3 + 2 \times \left(\frac{2.4}{1 - 0.8}\right) = 3 + 2 \times 12 = 27\text{ m}.

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