Question
Download Solution PDFA shopkeeper has 3 different qualities of Oil. 425 litres of 1st quality, 459 litres of 2nd quality and 493 litres of 3rd quality. Find the least possible number of bottles of equal size in which different oil of different qualities can be filled without any mixing.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Oil of 1st quality = 425 litres
Oil of 2nd quality = 459 litres
Oil of 3rd quality = 493 litres
Formula used:
To find the least possible number of bottles, we calculate the HCF (Highest Common Factor) of the given quantities.
Calculation:
HCF of 425, 459, and 493 using the Euclidean algorithm.
HCF of 425 and 459:
⇒ 459 ÷ 425 = 1 remainder 34
⇒ 425 ÷ 34 = 12 remainder 17
⇒ 34 ÷ 17 = 2 remainder 0
⇒ HCF(425, 459) = 17
HCF of 17 and 493:
⇒ 493 ÷ 17 = 29 remainder 0
⇒ HCF(17, 493) = 17
HCF of 425, 459, and 493 = 17
⇒ Number of bottles = Total oil ÷ HCF
⇒ Total oil = 425 + 459 + 493 = 1377 litres
⇒ Number of bottles = 1377 ÷ 17 = 81
∴ The correct answer is option (2).
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