Question

Madan purchases a compact computer system for $ Rs.{\text{ 47,700}} $ which includes \[10\% \] rebate on the marked price and then $ 6\% $ sales tax on the remaining price. Find the marked price of the computer.

Answer 1

Hint: The question is related to the marked prices and discounts sections. The question asks us to find the marked price of the compact computer system when its selling price is given and a specific rebate is also given along with a tax, First we will find the value of tax deducted so as to get the real selling price on which discount was calculated then solve it to find the marked price when the discount percent is given.

Complete step by step solution:
First let us find the tax deducted,
The system was sold for $ Rs.{\text{ 47,700}} $
The formula used is :
 $ {\text{Price before Tax }} = \dfrac{{{\text{Selling Price}}}}{{(100 + tax\% )}} \times 100 $
The selling price here is $ Rs.{\text{ 47,700}} $ , the tax percent given is $ 6\% $
So we get price before tax as,
 $ {\text{Price before Tax }} = \dfrac{{47700}}{{(100 + 6\% )}} \times 100 $
 $ {\text{Price before Tax }} = \dfrac{{47700}}{{106}} \times 100 $
 $ {\text{Price before Tax }} = 450 \times 100 $
 $ {\text{Price before Tax }} = Rs.45000 $
This is our real selling price which is resulted after the $ 10\% $ rebate(discount) on the marked price of compact computer system,
We have to find the marked price, the marked price when selling price and the discount percent is given will be calculated as,
 $ M.P. = \dfrac{{S.P.}}{{(100 - Discount\% )}} \times 100 $
 $ M.P. = \dfrac{{45000}}{{100 - 10}} \times 100 $
Upon solving the above equation further we get,
 $ M.P. = \dfrac{{45000}}{{90}} \times 100 $
 $ M.P. = 500 \times 100 $
 $ M.P. = 50000 $
This is the required value of the marked price, this is the price on which the discount was applied and then tax levied on it.
So, the correct answer is “Rs 50000”.

Note: The important point to note here is that we will first eliminate the tax component even though it is mentioned at last. Also remember that the tax formula written in the question
 $ {\text{Price before Tax }} = \dfrac{{{\text{Selling Price}}}}{{(100 + tax\% )}} \times 100 $
Is very similar to the formula for marked price, it is just applied in addition in the denominator of the formula, instead of the discount. So we can consider discount as negative and tax as positive in the denominator, the formula for marked price illustrates that,
 $ M.P. = \dfrac{{S.P.}}{{(100 - Discount\% )}} \times 100 $