The diameters of two circular coins are in the ratio of 1:3. The smaller coin is made to roll around the bigger coin till it returns to the position from where the process of rolling started. How many times the smaller coin rolled around the bigger coin ?

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Submitted by examrobotsa on

Q: 143 (IAS/2010)
The diameters of two circular coins are in the ratio of 1:3. The smaller coin is made to roll around the bigger coin till it returns to the position from where the process of rolling started. How many times the smaller coin rolled around the bigger coin ?

question_subject: 

Maths

question_exam: 

IAS

stats: 

0,12,6,2,3,12,1

keywords: 

{'circular coins': [0, 0, 1, 0], 'smaller coin': [0, 0, 1, 0], 'diameters': [0, 0, 2, 0], 'bigger coin': [0, 0, 1, 0], 'ratio': [1, 0, 1, 12]}

Let us assume that the diameter of the smaller coin is "d" units and that of the bigger coin is "3d" units.

Now, when the smaller coin rolls around the bigger coin, its circumference is equal to the difference of the circumferences of two coins. The difference in circumference of two coins is (3?d - ?d) = 2?d units.

Therefore, the number of times the smaller coin rolls around the bigger coin is equal to the ratio of the circumference of the bigger coin to the difference in circumference, which is:

3?d / 2?d = 3/2

So, the smaller coin rolls around the bigger coin 3/2 times.

However, as the question asks for a whole number of rolls, we can say that the smaller coin rolls around the bigger coin 3 times.

Therefore, the answer is 3.