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There is a car and a motor-bike. The car and the bike both have an spare tire. Now, the car has a total of 5 tyres (one spare tire included) and the bike has a total of 3 tires (one spare tire included).

Each tire of the bike and the car will last for 100 KMs. Take the following points into consideration:

  • The tire will not have any puncture or problem
  • The tire will rotate only when the vehicle moves.
  • Assume that petrol/diesel is infinite.
  • You cannot buy new tire.
  • Tires can be changed easily.
  • Once a tire has been used for travelling 100 KM, it cannot be used again.

Can the car or the bike travel further?

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Is this a trick question? It look just to be a math problem.

Answer:

The bike can travel further.

How to travel with bike:

The bike can travel 150 km = 100 km / 2 * 3 by rotating between its wheels. For each 50 km, two of the three wheels are used, so each wheel it used for two of the intervals.

How to travel with car:

The car can travel 125 km = 100 km / 4 * 5 by using a different four of the five wheels for each of five 25 km segments.

Alternative short argument:

Alternatively, the spare tire is a +1/4 relative increase in tire-power for the car and a +1/2 for the bike, so the bike wins.

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    $\begingroup$ The bike can also travel on one tire. ;) $\endgroup$ – Harv Jan 10 '15 at 10:13
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    $\begingroup$ @Harv And the car on 2 ;c) (...as proven in some movies...) $\endgroup$ – BmyGuest Jan 10 '15 at 10:29
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    $\begingroup$ @Xnor: I think it is just a math's puzzle. It may be rather easy, but I think it is a valid puzzle never-the-less and to be taken seriously. (The bike requires the 'change half-way' trick to be thought of.) Please put your answer in spoiler tags. $\endgroup$ – BmyGuest Jan 10 '15 at 10:32
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    $\begingroup$ The case with the motorcycle is similar to making three pieces of toast toasted on both sides with a toaster that can only toast two pieces one-sidedly at any one time. $\endgroup$ – h34 Jan 10 '15 at 14:54

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