Excess-shortage

Amount of water left is 0.1l short of filling a large container.

But it is more than enough to fill a small container, with 0.3l left over.

This tells you that the difference between a large and a small container's volume is :

0.1l + 0.3l = 0.4l

Thks for explaining. How abt b?

To add on for a), if it is hard to visualise, try to think about this scenario:

① Fill a small container completely. You have 0.3l leftover.

② Now you change your mind and decided to fill a large container instead. You would pour all the water from the small container into the large one.

③ You also pour the 0.3l you have left into the large container but it won't fill completely. Still need 0.1l.

④ Thinking about it, after you pour the water from the small container to the big one, you will need to fill an additional 0.3l + 0.1l = 0.4l.

Hence the difference must have been 0.4l.

Part b) will be explained in the next comment.

Great thanks! I totally understand why 0.3+0.1 is equal to diff after yr clear explanation. Initially still dont really understand, just tinking to memorise such steps if come across such question.

Question tells us that 4 identical large and 7 identical small containers are filled using 10.4l of water.

Now it is hard to proceed since we have two different types of containers.

So the idea now is, what if we switch all the 7 small containers to large ones?

We would need an additional volume of :
7 × 0.4l = 2.8l

So we would need 2.8l more water.

This is as good as saying we are filling 7 + 4 = 11 large containers.

2.8l + 10.4l = 13.2l

You could use 13.2l of water to fill 11 large containers.

Volume of 1 large container = 13.2l ÷ 11 = 1.2l


Now for the leftover over he has, it was 0.1l short of filling a large container.

So the volume of the leftover water must have been : 1.2l - 0.1l = 1.1l

Volume of water he has
= 10.4l he used to fill the 4 large and 7 small + 1.1l leftover water

= 11.5l

Thank you so much for detailed explanation! I finally can understand with your clear step by step workings with explanations. Great thks!

Or,

we could also imagine changing the 4 large containers to 4 small containers.

Now we have a total of 4 + 7 = 11 small containers

4 × 0.4l = 1.6l

1.6l less water is needed fill to them compared to 4 large and 7 small.

10.4l - 1.6l = 8.8l

8.8l is needed to fill 11 small containers.

1 small container has volume of :

8.8l ÷ 11 = 0.8l


Since the leftover water could fill 1 small container with 0.3l left over,

The leftover water volume = 0.8l + 0.3l = 1.1l

10.4l + 1.1l =11.5l (total water that Michael has)

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