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### Logic Puzzle Problem

Logic Puzzle Problem - 1 April

Like an usual car, my new i10 car has 5 wheels(2 front + 2 Rear + 1 spare).
Rear wheel of car will wear out after 21000 kilometers and front wheel will wear out after 29000 kilometers.

What is the maximum distance i can cover assuming changing of wheels is not an issues ?

1. 21000 kilometer, as usual......

2. Maximum distance : 30,450 kilometers.

For each 5 kilometers driven using this rotation, each tire will lose (2/29000)+(2/21000) of its tread.So, suppose we drive 5*N kilometers like this. Then, each tire will lose 2*N*((1/29000)+(1/21000)) of its tread. We wish to determine N so that the latter expression gets to be 1, representing all of each tire's tread. That happens when N=6090, which is when 5*N (the total kilometers driven) is 30,450

1. If we leave the spare alone and just rotate the four tires, they should average 25,000 miles each. Since we are rotating 5 tires instead of four, we should be able to get 31,250 miles from our tires.

25,000 * 5/4 = 31,250

3. Logic:
21000

4. 21,000kms

5. 21,000 kms answer cannot be right as rate of wearing of tyres are different for front and rear wheels.