UPSC Prelims 2007·GS1·economy·basic concepts

A Person has to completely put each of three liquids: 403 litres of petrol, 465 litres of diesel and 496 litres of the Mobil Oil in bottles of equal size without mixing any of the above three types of liquids such that each bottle is completed filled. What is the least possible number of bottles required?

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Last updated 23 May 2026, 3:31 pm IST
  1. A34
  2. B44Correct
  3. C46
  4. DNone of the above

Explanation

To find the least possible number of bottles, we must maximize the capacity of each bottle. This maximum capacity is the Highest Common Factor (HCF) of the three quantities: 403, 465, and 496. First, find the HCF: The difference between 465 and 403 is 62. The difference between 496 and 465 is 31. Since 31 is a factor of 62 and also divides 403, 465, and 496 exactly, the HCF is 31. This means each bottle will hold 31 litres. Next, calculate the number of bottles for each liquid: Number of petrol bottles = 403 divided by 31 = 13 Number of diesel bottles = 465 divided by 31 = 15 Number of Mobil Oil bottles = 496 divided by 31 = 16 Total number of bottles = 13 + 15 + 16 = 44. Therefore, the least possible number of bottles required is 44. Option B is correct.
economy: A Person has to completely put each of three liquids: 403 litres of petrol, 465 litres of diesel and 496 litres of the M
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