UPSC Prelims 2010 · General Studies
Question 113: Basic Numeracy
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 ?
AnswerThe answer is (c).
The coins have diameters in the ratio 1:3, so their circumferences are in the same ratio: the large coin's circumference is 3 times the small coin's. Rolling once round the big coin, the small coin travels a distance equal to the large circumference, which is 3 small circumferences, so by this measure it rolls 3 times. The given answer is 3.
How you could have got this
No shortcut here: in a “how many” question, ruling out options doesn’t help. Every statement has to be judged.
This follows an unofficial answer: UPSC has not published its key for this year, and if that answer is wrong, so is this path.
Which options go is worked out from UPSC’s key and the options, not by a model.
Why each option is right or wrong
- (a) 9 comes from squaring the ratio, which is for areas, not lengths.
- (b) 6 has no basis in the ratio of circumferences.
- (c) Right (as keyed): the circumference ratio is 3.
- (d) 1.5 has no basis in the ratio of circumferences.
Worth knowing: Strictly, the small coin turns 4 times on its own axis in one trip round the big coin, but 4 is not an option; the key counts the circumference ratio, 3.
Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2010, General Studies, Series A. The paper on upsc.gov.in.