Question

Three water containers contain 12 litres, 24 litres and 42 litres of water.

i. Find the maximum capacity of a measuring container that can fully measure the quantity of water in all three containers.

ii. Find out how many times this container needs to be filled to empty each container? ​

Answer 1

$\huge {\green {\underline {\mathfrak {Answer \: i}}}}$

There are three containers with 12l, 24l, and 42l of water.

So, the (assuming that the water is filled to the brim) the capacity of the containers are 12l, 24l, and 42l respectively.

Now, we need to calculate the maximum capacity of a measuring container that can fully measure the quantity of water in all three containers,

Therefore, to do so, we need to find out the HCF of them.

For 12 = 6 × 2

For 24 = 6 × 4

For 42 = 6 × 7

Hence, HCF is 6 (as it is repeated thrice in all the factors of the three numbers)

Therefore, your required answer is 6litres i.e., we need a measuring container of 6litres to measure the water in them completely.

$\huge {\blue {\underline {\mathfrak {Answer \: ii}}}}$

Now, in order to empty each container by using the measuring container, we need to empty them multiple times, because we can clearly see that 6 is smaller than all of them.

Therefore,

$\large {\underline {For \: 1st \: Container}}$

Divide 12 by 6

i.e., $\large {\frac{12}{6} }$

= $\large {2 }$

Thus we need to empty the first container 2 times to empty it fully by using the measuring container.

$\large {\underline {For \: 2nd \: Container}}$

Divide 24 by 6

i.e., $\large {\frac{24}{6} }$

= $\large {4}$

Thus we need to empty the second container 4 times to empty it fully by using the measuring container.

$\large {\underline {For \: 3rd \: Container}}$

Divide 42 by 6

i.e., $\large {\frac{42}{6} }$

= $\large {7}$

Thus we need to empty the third container 7 times to empty it fully by using the measuring container.

$\large {\underline {Shortcut \: Method }}$

We can observe that 2times, 4times and 7times are all factors of 12, 24, and 42 respectively. Thus instead of going into so much calculation, you can directly write that the remaining factors of 12, 24, and 42 (i.e., factors other than 6) as your answer.

Hope this helped you, thanks for posting :)