# A tin of flour weighs 10.5kg. When it is $\dfrac{1}{2}$ full, it weighs $5.375kg$. What is the weight of the empty tin?

Answer

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**Hint:**To solve the question we need to understand the problem and the condition given in the question. To solve this question we will write down all the values as per the given condition. The problem will be solved with the help of Algebraic operation.

**Complete step-by-step solution:**

The question asks us to find the value of the weight of the empty tin, when a tin full of flour weighs $10.5kg$ and half of the full weight $5.375kg$. The first step for this question is to write up all the conditions which are given in the question.

Tin full of flour =$10.5kg$

$\Rightarrow $ Weight of tin + weight of flour ( full tin) $=10.5kg$

Weight when tin is half full of flour$=5.375kg$

$\Rightarrow $ Weight of tin + weight of flour half tin) $=5.375kg$

To find the weight of flour half full we will have to subtract the above two equations. On doing this we get:

$\Rightarrow $ Weight of flour( full tin) - Weight of flour( half tin) $=10.5kg-5.375kg$

$\Rightarrow $ Weight of flour( full tin) - Weight of flour( half tin) $=5.125kg$

So the weight of the half full flour is $5.125kg$.

Now the next step is to find the weight of the empty tin. With all the information given to us the equation which we will use to find the weight is:

$\Rightarrow $ Weight of tin + Weight of flour half filled $=5.375kg$

On substituting the value we get:

$\Rightarrow $ Weight of tin +$5.125kg$ $=5.375kg$

$\Rightarrow $ Weight of tin $=5.375kg-5.125kg$

$\Rightarrow $ Weight of tin $=0.250kg$

**$\therefore $ The weight of the tin is $0.250kg$.**

**Note:**We can even check whether the answer is correct or not. For this we will use the formula Weight of tin+ Weight of half filled flour, if its value comes the same as that given in the question which is $5.375kg$ then the answer is correct. So on substituting the values in the formula we get:

$\Rightarrow $ Weight of tin+ Weight of half filled flour

$\Rightarrow 0.250kg+5.125kg$

$\Rightarrow 5.375kg$

Since the values are the same which means the answer is correct.

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