UPSC Prelims 2007 · General Studies
Question 144: Basic Numeracy
A person has to completely put each of three liquids – 403 litres of petrol, 465 litres of diesel and 496 litres of mobile oil – in bottles of equal size without mixing any of the three types of liquids such that each bottle is completely filled. What is the least possible number of bottles required?
AnswerThe answer is (b).
Each bottle must be filled exactly and hold only one liquid, so its size must divide 403, 465 and 496. For the fewest bottles, take the largest such size, the HCF. 403 = 13 x 31, 465 = 15 x 31, 496 = 16 x 31, so the HCF is 31 litres. Bottles needed: 13 + 15 + 16 = 44.
Why each option is right or wrong
- (a) 34 is too few; the count is 44.
- (b) Correct: 13 + 15 + 16 = 44.
- (c) 46 is too many; a 31-litre bottle needs only 44.
- (d) Option (b) gives the answer, so 'none' fails.
Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2007, General Studies. UPSC's own paper isn't online; the words are from a published compilation. The paper on upsc.gov.in.