A merchant has 120 litres of oil 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 tin of equal capacity, what should be the greatest capacity of such a tin ?
Answers
Answer:
The merchant needs to fill 60 liters of all types of oils
Step-by-step explanation:
We need to find the HCF or GCD that is Greatest Common Divisor
120=2×2×2×3×5
180=2×2×3×3×5
240=2×2×2×2×3×5
GCD=2×2×3×5=60
The greatest capacity = 60 liters
So the merchant needs to fill 60 liters of all types of oils
Step-by-step explanation:
We need to arrange tins of capacity such that all tins are filled to the top and no oil is left.
If we order tins of 120 l each then then some tins will not be filled to the top because the second oil and third oil will not be completely distributed in 120 l capacity of tins.
Therefore for this we need to find a capacity that will divide all three numbers that is 120 180 and 240
2 can divide all the given numbers. So we can order cans of 2 litres each.
But is 2 the highest or maximum factor/number which can divide all the given Numbers?
Of course not !
because we know that 10 can also Divide all the given numbers
So what will be the greatest number which can divide all the three given numbers?
For this we need to find Highest Common Factor (HCF)
HCF = 60
So The maximum capacity of such a tin is 60 litres.
