Question

Amit goes to a shop to buy a washing machine. The marked price of the washing machine is Rs. $10900$ excluding $9\%$ VAT. Amit bargains with the shopkeeper and convinces him for Rs. $10900$ including $9\%$ VAT as the final cost of the washing machine. Find the amount reduced by the shopkeeper.

Answer 1

Hint: We will first assume the reduced price to be a variable then we will calculate the VAT on it by applying the rate given in the question and after that, we will calculate the final amount that needs to be paid to the shopkeeper and equate it with the given the marked price. In this way, we will get the reduced price of the machine and finally, we will subtract it from the MP of the machine to get the amount reduced by the shopkeeper.

Complete step-by-step solution:
Marked price refers to the price which is written on the product. This is the price at which the product is intended to sell. VAT is basically a type of tax that we need to pay in addition to the marked price.
We see that the marked price of the washing machine is given, therefore:
M.P. = Rs. $10900$
Rate of VAT = $9\%$
Let the reduced price of the washing machine be: Rs. $x$,
Now, we know that the VAT at the rate of $9\%$ will be = $9\%$ of $x$ = $x\times \dfrac{9}{100}=\dfrac{9x}{100}$
So the total amount paid will be = $x+\dfrac{9x}{100}=\dfrac{109x}{100}$
Now, we will equate the amount paid to the marked price as Amit convinced the shopkeeper for Rs. $10900$, So : $\dfrac{109x}{100}=10900\Rightarrow x=\dfrac{10900\times 100}{109}$
Therefore, $x=10000$.
Amount reduced by the shopkeeper is = $M.P.-x=10900-10000=900$
Therefore, the amount reduced by the shopkeeper is Rs. $900$.

Note: There can be some discount given on the marked price and the actual selling price of the product may be less than the marked price. It is generally denoted by MP. When a discount is offered, then M.P. > S.P. and when the discount is not offered, M.P. < S.P.