question_answer

A merchant has 120 litres of oil of one kind, 180 litres of another kind and 240 litres of a third kind. He wants to sell the oil by filling the three kinds of oil in tins of equal capacity. What should be the greatest capacity of such a tin?

Answer:

The greatest capacity of the required measure will be equal to the HCF of 120,180 and 240 L. Prime factorisation of 120,180 and 240

2	120
2	60
3	30
5	15
5	5
	1

2	180
2	90
3	45
5	15
5	5
	1

2	240
2	120
2	60
3	30
5	15
5	5
	1

\[120=2\times 2\times 2\times 3\times 5\] \[180=2\times 2x\times 3\times 3\times 5\] \[240=2\times 2\times 2\times 2\times 3\times 5\] Common factors of 120, 180 and\[240=2\times 2\times 3\times 5=60\] Hence, greatest capacity of tin = 60 L.