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 such a tin?

• A. $20$ liters
• B. $30$ liters
• C. $60$ liters
• D. $80$ liters

Answer 1

The correct option is C $60$ liters

$\text{We need to find the HCF or GCD that is Greatest Common Divisor}$

$120=2\times 2\times 2\times 3\times 5$

$180=2\times 2\times 3\times 3\times 5$

$240=2\times 2\times 2\times 2\times 3\times 5$

$GCD=2\times 2\times 3\times 5=60$

$\text{The greatest capacity = 60 liters}$

$\text{So the merchant needs to fill 60 liters of all types of oils}$

$\text{Hence option C is correct}$