Question

A merchant has 120 litres of oil of one kind, 180 litres of another kind and 240 litres of 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

Quantity of oil A = 120 liters
Quantity of oil B = 180liters
Quantity of oil C = 240liters
We want to fill oils A, B and C in tins of the same capacity

∴ The greatest capacity of the tin chat can hold oil. A, B and C = HCF of 120, 180 and 240
By fundamental theorem of arithmetic
120 = 2³ × 3 × 5
180 = 2² × 3² × 5
240 = 2⁴ × 3 × 5
HCF = 2² × 3 × 5 = 4 × 3 × 5 = 60 litres
The greatest capacity of tin = 60 litres