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 above three types of liquids such that each bottle is completely filled. What

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Q: 54 (IAS/2007)
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 above three types of liquids such that each bottle is completely filled. What is the least possible number of bottles required?

question_subject: 

Logic/Reasoning

question_exam: 

IAS

stats: 

0,2,5,3,2,1,1

keywords: 

{'litres': [0, 0, 2, 1], 'liquids': [0, 0, 0, 1], 'least possible number': [0, 0, 1, 0], 'bottles': [0, 1, 1, 1], 'bottle': [0, 2, 1, 2], 'petrol': [2, 0, 1, 5], 'diesel': [1, 0, 0, 1], 'mobile oil': [0, 0, 1, 0], 'equal size': [0, 0, 1, 0], 'none': [2, 0, 8, 15]}

To find the least possible number of bottles required to store the given quantities of liquids without mixing them, we need to find the greatest common divisor (GCD) of the three quantities.

The GCD of the three quantities (403, 465, and 496) can be calculated by finding the GCD of the pairwise combinations and repeating the process until all three numbers are considered together.

GCD(403, 465) = 31

GCD(31, 496) = 31

Hence, the GCD of 403, 465, and 496 is 31.

To find the number of bottles required, we divide each quantity by the GCD and then sum up the quotients:

403 / 31 = 13

465 / 31 = 15

496 / 31 = 16

The sum of the quotients is 13 + 15 + 16 = 44.

Therefore, the least possible number of bottles required to store the given quantities of liquids without mixing them is 44.

The correct option is Option 2: 44.

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