Take a close look at both scales before you decide on an answer.
At first glance, this puzzle looks very simple.
But if you rush, you might miss one important detail.
The numbers seem easy to compare, yet the jars are not filled the same way.
That is exactly what makes this puzzle interesting.
Your goal is not to guess.
Your goal is to use logic.
Start with the first scale.
It shows one completely full jar.
The total weight is 120 grams.
Remember that this weight includes two things.
It includes the weight of the glass jar itself.
It also includes everything inside the jar.
Now move to the second scale.
This time, there are two jars.
One jar is empty.
The other jar is only half full.
Together, they weigh 150 grams.
The trick is to separate the weight of the jars from the weight of the liquid.
Do not treat the liquid and the jar as one object.
Think about them as two different parts.
If a full jar weighs 120 grams, then half of the liquid weighs exactly half as much as the full amount of liquid.
The glass jar itself does not become lighter or heavier.
Only the amount of liquid changes.
That is the key idea.
Many people make the mistake of comparing 120 grams and 150 grams directly.
That approach does not work.
Instead, give each unknown a name.
Imagine the empty jar has one weight.
Imagine the full amount of liquid has another weight.
The first picture gives you one equation.
The second picture gives you another equation.
Now compare the two equations carefully.
Notice that one equation contains one jar and one full amount of liquid.
The other equation contains two jars and only half of the liquid.
That difference is all you need.
You do not need any extra information.
Everything required to solve the puzzle is already shown in the picture.
Take your time.
Subtract what is the same.
Keep track of what is left.
Avoid skipping steps.
A small mistake with the half-full jar will lead to the wrong answer.
Once you find the weight of the liquid, the weight of the empty jar becomes easy to calculate.
There is only one correct answer.
If your numbers satisfy both scales, then your solution is correct.
The empty jar weighs 60 grams.
Here’s why.
Let J be the weight of the empty jar.
Let L be the weight of the liquid when the jar is completely full.
From the first scale:
J + L = 120
From the second scale:
2J + ½L = 150
Since L = 120 − J, substitute it into the second equation.
2J + ½(120 − J) = 150
2J + 60 − ½J = 150
1.5J = 90
J = 60
