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# Find the rate of VAT if amount Rs. 45 was paid for the list price of a pair of shoes of Rs. 450.

Last updated date: 21st Jul 2024
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Hint: We need to assume the percentage value of 45 out of 450. We multiply 450 with the percent value to find the value of 45. We find the mathematical form and solve the equation to find the value of the assumed variable.

The amount of VAT was Rs. 45 for the list price of a pair of shoes of Rs. 450.
We need to find the rate which can be expressed as percentage value.
We need to find the percentage value of 45 out of 450.
We assume that x% of 450 is 45.
The fraction is the respective ratio of two numbers. We find the value of the numerator with respect to the denominator of the fraction.
In case of percentage, we need to convert the denominator of the fraction into 100.
The numerator of the fraction with denominator being 100 will be the solution of the problem.
Therefore, x% can be written as $\dfrac{x}{100}$ .
Now x percent of 450 is 45. Forming the mathematical expression, we get $450\times \dfrac{x}{100}=45$ .
We now solve the equation to get
\begin{align} & 450\times \dfrac{x}{100}=45 \\ & \Rightarrow x=45\times \dfrac{100}{450} \\ \end{align}
We complete the multiplication and get $x=45\times \dfrac{100}{450}=\dfrac{100}{10}=10$ .
The rate of VAT is 10%.
So, the correct answer is “10%.”.

Note: The value of the fraction is actually the unitary value of x out of 100. Therefore, in percentage value we got 10 as the percentage. Percentage deals with the ratio out of 100. The ratio value for both fraction and percentage is the same.