Question

Two tankers contain 850 litres and 680 litres of kerosene oil respectively. Find the maximum capacity of a container which can measure the kerosene oil of both the tankers when used an exact number of times.

Answer 1

The required container has to measure both the tankers in a way that a count is an exact number of times. So its capacity must be an exact divisor of the capacities of both the tankers. Moreover, this capacity should be maximum. Thus, the maximum capacity of such a container will be the HCF of 850 and 680.

 

Hence,

850 = 2 × 5 × 5 × 17= 2 × 5 × 17 × 5 and

680 = 2 × 2 × 2 × 5 × 17= 2 × 5 × 17 × 2 × 2

The common factors of 850 and 680 are 2, 5 and 17.

Thus, the HCF of 850 and 680 is 2 × 5 × 17 = 170.

Therefore, the maximum capacity of the required container is 170 liters.

It will fill the first container in 5 and the second in 4 refills.