Greatest Capacity of a Tin for 120, 180 and 240 Liters of Oil

Video Explanation

Watch the video below to understand the complete solution step by step:

Solution

Question: A merchant has 120 liters of oil of one kind, 180 liters of another kind and 240 liters 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?

Step 1: Identify the Mathematical Concept

The greatest capacity of the tin that can exactly divide all three quantities is the HCF (Highest Common Factor) of 120, 180 and 240.

Step 2: Find the HCF Using Euclid’s Division Algorithm

180 = 120 × 1 + 60

120 = 60 × 2 + 0

So, HCF (120, 180) = 60

Now find HCF of 60 and 240:

240 = 60 × 4 + 0

So, HCF (60, 240) = 60

Final Answer

∴ The greatest capacity of the tin is 60 liters.

Conclusion

Thus, by using Euclid’s division algorithm, we find that the maximum capacity of each tin should be 60 liters.