Question

A merchant has 120 liters of oil of one kind, 180 liters of another kind and 240 liters 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?
$
  {\text{A}}{\text{. }}20{\text{ litre}} \\
  {\text{B}}{\text{. }}30{\text{ litre}} \\
  {\text{C}}{\text{. }}60{\text{ litre}} \\
  {\text{D}}{\text{. }}80{\text{ litre}} \\
 $

Answer 1

Hint: Here we have to go through by finding the highest common factor which is also known as HCF. Because we have to find out the greatest capacity of tin so that all kinds of oil satisfy it.

Complete step-by-step answer:
Here in the question it is given that,
Quantity of oil A = 120 liters
Quantity of oil B = 180 liters
Quantity of oil C = 240 liters
We want to fill oils A, B and C in tins of the same capacity
Therefore the greatest capacity of tin that can hold oil A, B and C = taking the highest common factor (HCF) of all the tanks volume.
I.e. HCF of 120,180 and 240.
We are finding HCF because it has asked us about the greatest capacity of tin.
By fundamental theorems of arithmetic,
$
  120 = 2 \times \times 2 \times 2 \times 3 \times 5 \\
  180 = 2 \times 2 \times 3 \times 3 \times 5 \\
  240 = 2 \times 2 \times 2 \times 2 \times 3 \times 5 \\
 $
And we know that HCF means taking the highest common factor of all.
I.e. HCF=$2 \times 2 \times 3 \times 5 = 60$
So the greatest capacity of tin = 60liters

So, the correct answer is “Option C”.

Note: whenever we face such a type of question the key concept for solving the question is whenever you have to ask about the greatest quantity you have to find out the HCF and whenever it asks about the lowest quantity you have to find out the LCM.