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

Given: A merchant has 120 litres of oil of one kind, 180 litres of another and 240 litres of the third kind.

To find: Here we have to find the greatest capacity of the tin.

Solution:

Given that the merchant wants to sell the oil by filling the three kinds of oil in tins of equal capacity.

To find the greatest capacity of such a tin we need to calculate the HCF of 120, 180 and 240.

First, let's find HCF of 120 and 180 using Euclid's division algorithm:

Using Euclid’s lemma to get:
• $180\ =\ 120\ \times\ 1\ +\ 60$

Now, consider the divisor 120 and the remainder 60, and apply the division lemma to get:
• $120\ =\ 60\ \times\ 2\ +\ 0$

The remainder has become zero, and we cannot proceed any further.

Therefore the HCF of 120 and 180 is the divisor at this stage, i.e., 60.

Now, let's find HCF of 60 and 240 using Euclid's division algorithm:

Using Euclid’s lemma to get:
• $240\ =\ 60\ \times\ 4\ +\ 0$

The remainder has become zero, and we cannot proceed any further.

Therefore the HCF of 60 and 240 is the divisor at this stage, i.e., 60.

So, HCF of 120, 180 and 240 is 60.

The greatest capacity of the tin for filling three different types of oil is 60 litres.

Updated on: 10-Oct-2022

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