Problem Solving

A car runs on four tyres and has one extra tyre. If each tyre lasts for 10,000 km then what is the
maximum distance (in km) that the car can travel using the five tyres?
(a) 10,000 (b) 11,000 (c) 12,500 (d) 15,000

sanjoy18 wrote:A car runs on four tyres and has one extra tyre. If each tyre lasts for 10,000 km then what is the
maximum distance (in km) that the car can travel using the five tyres?
(a) 10,000 (b) 11,000 (c) 12,500 (d) 15,000

Sanjoy,
Since each tyre can run upto 10,000km and with four wheel.
So extra tyre of 10,000km can be equally divided into remaining four tyres
10,000/4 = 2500

so totally 10,000+2500 = 12,500

Hence OA C

Regards,
Uva.

The car travels in whole, that is on all 4 tyres. So suppose the car travels for 10 k km, then all the four tyres are worn out, so even if one tyre is replaced, the car cannot travel further. So 10000 km is the max distance it can travel. A

vinay1983 wrote:The car travels in whole, that is on all 4 tyres. So suppose the car travels for 10 k km, then all the four tyres are worn out, so even if one tyre is replaced, the car cannot travel further. So 10000 km is the max distance it can travel. A

Vinay, what if we keep on changing the tires at an interval of 2500Km?

vinay1983 wrote:The car travels in whole, that is on all 4 tyres. So suppose the car travels for 10 k km, then all the four tyres are worn out, so even if one tyre is replaced, the car cannot travel further. So 10000 km is the max distance it can travel. A

Hi Vinay,
I Guess 10,000 Km can't be MAX distance.

Why do you consider they will replace the Tyre after driving complete 10,000 Km.

Consider the situation where they will replaced Tyre for each and every kilometer(Sounds weird, But possible or once in 2500 Km )

so extra 2500 kilometer will be added.

Correct me if I am wrong.

Regards,
Uva.

sanjoy18 wrote:A car runs on four tyres and has one extra tyre. If each tyre lasts for 10,000 km then what is the
maximum distance (in km) that the car can travel using the five tyres?
(a) 10,000 (b) 11,000 (c) 12,500 (d) 15,000

Let the 5 tires be = A, B, C, D, E.
If we swap out a tire every kilometer -- so that, for each kilometer traveled, a different tire is not used -- the usage per tire over the first 5 kilometers will look as follows:

A B C D E
1 1 1 1 0
1 1 1 0 1
1 1 0 1 1
1 0 1 1 1
0 1 1 1 1

Result:
Usage per tire = 4 kilometers.
Distance traveled = 5 kilometers.
Implication:
For every 4 kilometers of tire usage, 5 kilometers can be traveled.

Since each tire can be used for up to 10,000 kilometers, we get:
(4 kilometers usage)/(5 kilometers traveled) = (10,000 kilometers usage)/(x kilometers traveled)
4x = 50,000
x = 12,500.

The correct answer is C.