Question

Three jars of milk contains 40 litres 50 litres and 60 litres of milk. Find the greatest capacity of a vessel which can empty out each jar with the exact number of fillings.​

Answer 1

to find:

$\tt{the\: maximum\: capacity \: of \: the \: vessel \: that\: can \:hold }$

given :

$\bull \: \tt{capacity \:of \:1st \:conatiner = 40 \: l }$

$\bull \: \tt{capacity\: of \: the\: 2nd \: container =50 \: l}$

$\bull \: \tt{capacity\: of\: the\: 3rd\: container = 60\: l}$

solution :

$\tt{ to \: find\: the\: highest \: capacity\: , \: we \: have\: to\: calculate \:the\: HCF}$

$\tt{HCF \: of \: 40\:l, \: 50 \:l \: and\: 60 \:l$

$\tt{\implies \: 40 = 2\times2\times2\times5$

$\tt{\implies \: 50 = 2\times5\times5}$

$\tt{\implies \: 60 = 2\times2\times3\times5$

$\tt{\implies\: the\: HCF = 2\times 5$

$\tt{\implies \: the \: HCF = 10 }$

$\tt{hence, \: the \: maximum \: capacity \: of \: vessel \: is \: 10\:l}$

additional information :

• when any question ask about highest quantity or capacity, most probably it is asking the HCF of the given quantities .
• when any question is asking about the least quantity related with the given quantity, most probably it is asking the LCM of the given quantity .

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Answer 2

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