Question

A blazer is Marked in a shop for rupees 2464, the rate of tax is 12%. Aakriti tells the shopkeeper to lower the rate to an extent that she has to pay nothing more than rupees 2464 including tax. Find the reduction required.

Answer 1

Hint: We assume the deducted amount to be $x$ rupees. We have the new marked price as $LP=\left( 2464-x \right)$rupees and tax amount $T=\dfrac{T\%}{100}\times LP=\dfrac{12}{100}\times \left( 2464-x \right)$. We equate the new selling price $SP=LP+T=LP+12\%\times LP$ to given 2464 and then solve for $x$. \[\]

Complete step-by-step solution
The price that is shown on goods or services is called list or marked price (LP) and the price on which that has to be sold to the customer is called selling price (SP). We also know that tax is the amount added to the marked price which goes to the government. So the relation between tax $\text{T}$, selling price, and the market price is
\[\begin{align}
  & SP=LP+T \\
 & \Rightarrow LP=SP-T \\
\end{align}\]
If the tax calculated in percentage is called tax rate. If the tax rate is $T\%$ then the tax amount is given by,
\[T=\dfrac{T\%}{100}\times LP\]
We are given the question that blazer is Marked in a shop for rupees 2464 rate of tax is 12%. So we have $LP=2464$ rupees and $\%T=12$. We are further given that Aakriti tells the shopkeeper to lower the rate to an extent that she has to pay nothing more than rupees 2464 including tax. We are asked to find the reduction amount.
Let us assume the reduction amount to be $x$ rupees. So the new market price for shopkeepers is $\left( 2464-x \right)$ rupees. There is 12% tax to be included on the new marked price. So the tax amount is
\[T=\dfrac{T\%}{100}\times LP=\dfrac{12}{100}\times \left( 2464-x \right)\]
So the new selling price will be
\[\Rightarrow SP=LP+T=\left( 2464-x \right)+\dfrac{12}{100}\times \left( 2464-x \right)\]
We are given that this price is Rs.2464. So we have,
\[\begin{align}
  & \Rightarrow SP=\left( 2464-x \right)+\dfrac{12}{100}\times \left( 2464-x \right)=2464 \\
 & \Rightarrow \left( 2464-x \right)\left( 1+\dfrac{12}{100} \right)=2464 \\
 & \Rightarrow 2464-x=2464\times \dfrac{100}{112}=2200 \\
 & \Rightarrow x=2464-2200=264 \\
\end{align}\]
So the reduction amount is 64 rupees.

Note: We note that the key in this question is the ambiguous phrase ‘Rs 2464 include tax’. Most mistakes happen by calculating the original selling price while calculating the tax percentage on the original marked price and then subtracting the new selling price. We note that the deducted amount is also called discount and the discount rate here will be calculated on market price.