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 a such a tin.

Answer 1

We need to find the GCD-that is Greatest Common Divisor 

gcd(120,180,240) = 60 

So the merchant needs to fill 60 liters of all types of oils that is 3 times the gcd
=> 60*3 = 180 liters will used in filling all of the 3 equal tin containers.

The greatest capacity = 60 liters

Hope This Helps :)

Answer 2

Answer:

From the question, it’s given that the merchant has 3 different oils of 120 litres, 180 litres and

240 litres respectively.

So, the greatest capacity of the tin for filling three different types of oil can be found out by

simply finding the H.C.F. of the three quantities 120,180 and 240.

Firstly, apply Euclid’s division lemma on 180 and 120.

180 = 120 x 1 + 60

120 = 60 x 2 + 0 (here the remainder becomes zero in this step)

Since the divisor at the last step is 60, the HCF (120, 180) = 60.

Now, let’s find the H.C.F of 60 and the third quantity 240.

Applying Euclid’s division lemma, we get

240 = 60 x 4 + 0

And here, since the remainder is 0, the HCF (240, 60) is 60.

Therefore, the tin should be of 60 litres.

Step-by-step explanation: