A student uniform showroom gives a 10% discount on the uniform of Rs.700 and charges 5% GST on the remaining amount, then what is the purchase price of the uniform for the customer? \[\]

Hint: We have been given the rate of discount, listed price and tax rate of single uniform respectively as $\%D=10,LP=700,T\%=5$ . We find the amount discount $\text{D}=\dfrac{\%\text{ D}}{\text{LP}}\times 100$, the selling price $SP=LP+D$, the tax amount $\text{T}=\dfrac{\%\text{ T}}{\text{SP}}\times 100$ and finally the required purchasing price $PP=SP+T$. \[\]

Complete step by step answer:
We know that discount is the amount of that is deducted from price shown on goods or services, for example in restaurants, sales, marts etc. The price that is shown on goods or services is called list price (LP) and the price on which that is sold to the customer is called selling price (SP). The relation between discount D, list price (LP) and selling price (SP) is given by,
\[\text{D}=\text{LP}-\text{SP}\]
We also know that tax is the amount added to selling price to which goes to the government. The purchase price PP of customer is sum of tax amount and selling price. So the tax is given by
\[PP=SP+T\]
The discount in percentage called rate of discount. If the rate of discount is $D\%$ then discount amount is,
\[\text{D}=\dfrac{\text{ }\!\!\%\!\!\text{ D}}{\text{LP}}\times 100\]
The tax amount in percentage is called tax rate. If tax rate is $T\%$ then the tax amount is,
\[T=\dfrac{T\%}{100}\times \text{SP}\]
We are given the question that a student uniform showroom gives 10% discount on the uniform of Rs.700 and charges 5% GST on the remaining amount. So we have the rate of discount, listed price and tax rate of single uniform respectively as
\[\%D=10,LP=700,T\%=5\]
We find the amount of discount in rupees as
\[\text{D}=\dfrac{\text{ }\!\!\%\!\!\text{ D}}{\text{100}}\times LP=\dfrac{10}{100}\times 700=70\]
We find the selling price in rupees as,
\[\begin{align}
  & \text{D}=\text{LP}-\text{SP} \\
 & \Rightarrow 70=700-\text{SP} \\
 & \Rightarrow \text{SP}=700-70=630 \\
\end{align}\]
We find the tax amount using tax rate and selling prices as,
\[T=\dfrac{T\%}{100}\times \text{SP}=\dfrac{5}{100}\times \text{630}=31.5\]

We find the purchase price in rupees as,
\[\text{PP}=\text{SP}+\text{T}=\text{630}+31.5=661.5\]

Note: We note that the discount rate is calculated on list or marked price $\left( D\%=\dfrac{D}{LP}\times 100 \right)$ and tax rate is calculated on selling price after the deduction of discount $\left( T\%=\dfrac{T}{SP}\times 100 \right)$. Students make mistakes here by calculating the tax rate on list price instead of selling price. GST is the acronym for goods and services tax, tax by Indian government.