Question

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 1

A merchant has 3 kinds of oil with different quantities like 120 litres, 180 litres and 240 litres.

Since, he wants to sell the oil by filling the three kinds of oil in tins of equal capacity, so the greatest capacity of such a tin is the HCF of 120, 180 and 240.

2	120
2	60
2	30
3	15
5	5
	1

 

2	180
2	90
3	45
3	15
5	5
	1

 

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

Now 120 = 2 × 2 × 2 × 3 × 5

180 = 2 × 2 × 3 × 3 × 5

240 = 2 × 2 × 2 × 2 × 3 × 4

∴ The required greatest capacity of a tin = (2 × 2 × 3 × 5) litres = 60 litres