DILR Puzzle | Car, Wheels and Distance3 min read

DILR Puzzles make us think and exercise our brains. It is the the weekend now and I hope some of you are looking to utilize some time for your CAT Preparation. Here’s a small but elegant DILR puzzle for you to solve, with a detailed solution given below. Happy solving!

You might also want to check out 2IIM’s Free Question Bank with many many questions from Quant, VARC and DILR with detailed solutions. For more resources from 2IIM, check out this wonderful article that talks about out last mile resources. 🙂

DILR Puzzle – Question

You have a car with 4 wheels, where each of these wheels can run for 400 kms. You also have a spare wheel in your storage with the same running capacity of 400 kms as the other wheels.

What is the maximum distance you can travel?

Take some time and solve this interesting question!

DILR Puzzle – Decoded

I hope all of you had fun solving this. Let us now look at the decoding of the elegant puzzle with this detailed solution given below.

First, let us name the tyres A,B,C,D and R (Spare Tyre). Each tyre can travel a maximum distance of 400 kms.

Suppose we change one tyre after travelling 100 kms.

Let us tabulate the data, capturing the distance remaining for each tyre. Tyres which are used in the particular 100 km segment are highlighted in blue.

As you can see in the table above, after 100 kms, we switch out tyre A for R and store tyre A in the storage of the car. As of this moment, A,B,C,D have 300kms left on them while R has a full capacity of 400 kms.

After 200 kms, we switch out tyre B for tyre A. All the tyres except A and R have only half their capacity left ie. 200kms.

After 300 kms, we switch out tyre C for tyre B and after 400 kms, D is the only wheel that hasn’t been replaced yet. Our journey feels like it must have reached its end…but no! We still have tyre C with 100kms capacity left, so we take the weared out tyre D and replace it with C.

Now, all wheels have a capacity of 100 kms left in them, AFTER 400 kms.

Therefore, the maximum distance you can travel with this car, its 4 wheels and a spare tyre, is 500 kms.

I hope you had fun solving this DILR Puzzle. For more puzzles and games that sharpen your brain, check out this article that talks about 5 puzzle games that optimize your brain for CAT!

Stay Safe, Best Wishes for CAT.

Rajesh Balasubramanian takes the CAT every year and is a 4-time CAT 100 percentiler. He likes few things more than teaching Math and insists to this day that he is a better teacher than exam-taker.