A man is riding a bike with front and back wheel circumference of 40 inches…

2023

A man is riding a bike with front and back wheel circumference of 40 inches and 70 inches respectively. If the man rides the bike on a straight road without slippage, how many inches will the man have travelled when the front wheel has made 15 revolutions more than the back wheel?

  1. A.

    1100

  2. B.

    1200

  3. C.

    1400

  4. D.

    1234

Attempted by 2 students.

Show answer & explanation

Correct answer: C

Step-by-Step Solution

Since the bike travels on a straight road without slippage, the total distance traveled by both the front and back wheels must be equal.

  1. Define variables:

    • Let n be the number of revolutions made by the back wheel.

    • The number of revolutions made by the front wheel is then n + 15.

    • Front wheel circumference (Cf) = 40 inches.

    • Back wheel circumference (Cb) = 70 inches.

  2. Equate the distances:

    • Distance = Circumference * Number of Revolutions.

    • Distance traveled by front wheel = Distance traveled by back wheel.

    • 40 * (n + 15) = 70 * n.

  3. Solve for n:

    • 40n + 600 = 70n.

    • 600 = 30n.

    • n = 20 (revolutions of the back wheel).

  4. Calculate the total distance:

    • Total distance = 70 * 20 = 1400 inches.

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