SAT entrance Problem

Hello math bugs(🐞) and hivers(🐝)
I hope your are strong and stout & doing good in life.

Today I have come up with a very intersting problem. If you are fetching the problem for the first time, chance is 99% you fail. It is look very easy to solve but believe me it's not.

This is a question of SAT entrance exam and no candidate answered it correctly. It was a MCQ and none of the option was correct. That's why even briliant failed to answer.

Without further ado, let's do it.
And is very simple: 12÷4 +1= 4 🤣

So, the smaller circle will make 4 revolution around the larger one sticking it to come back at start point of contact.

To understand the logic behind it, we need to recap time and distance simple concept as follows:

✅ If a train Crosses a man or a pole or a tree, total distance covered the train equals to the length of the train. Check the photo given below: Source [Edited by me.]

✅✅ If a train Crosses a station or a bridge, total distance covered by the train will be the sum of the lengths of the train and the station (bridge). Source [Edited by me]

Here in today's problem total distance(D) must be the sum of perimeters of the two given circle. So, the answer of the problem will be (D÷ perimeter of small circle) and this is equal to 4. Or Number of revolution = (2πR+ 2πr)÷2πr where R = 12 cm and r= 4 cm

LET'S TRY IT PRACTICALLY:

Still you may have doubt. Don't worry I have a solution to clear your doubt. Take two coins of same radius, set them as shown in the problem(cover) figure, make a mark with a marker pen on the point of contact. Then try to revolve it. You will see Answer will be 2 revolutions but before doing it practically,it seemed it would take just one revolution. Source [Edited by me]

Check carefully 1/4 perimeter in coin one(1) and 1/2 distance in coin two (2) are covered as shown in the above picture. Thus, perimeter of coin one (1) and twice perimeter in coin two (2) will be covered.So, Coin two will make two revolution in total to come back it's starting point.

I hope you have enjoyed today's concept.

Thank you so much for stoping by

Have a good day

All is well.

Regards: @meta007