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?


1 Answer 1


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


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.

  • 3
    $\begingroup$ The bike can also travel on one tire. ;) $\endgroup$
    – Harv
    Jan 10, 2015 at 10:13
  • 1
    $\begingroup$ @Harv And the car on 2 ;c) (...as proven in some movies...) $\endgroup$
    – BmyGuest
    Jan 10, 2015 at 10:29
  • 2
    $\begingroup$ @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, 2015 at 10:32
  • 2
    $\begingroup$ 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, 2015 at 14:54

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.