Question

The catalogue price of a computer set is Rs 42,000. The shopkeeper gave a discount of 10% on the listed price. He further gives an off-season discount of 5% on the discounted price. However, sales tax at 8% is charged on the remaining price after two successive discounts.
Find:
(i) The amount of sales tax a customer has to pay.
(ii) The total amount to be paid by the customer for the computer set.

Answer 1

Hint: We will solve this question using simple formulas of Profit, loss and discount. However, we would take off the amount on which the discount is being applied and similarly the sales tax is being applied and then work according to the question.

Complete step-by-step answer:

Given that the list price of the computer set is Rs 42,000.

Let us assume the following variables-

Cp stands for the cost price or the catalogue price.
$SP_1$ stands for the sale price without tax.
$SP_2$ stands for the sales price with tax.
$D_1$ stands for the first discount that is being applied.
$D_2$ stands for the second discount that is being applied.

(i) First of all we calculate the amount after deducting first rate of discount i.e. $D_1$ =10% . We have the formula to do so as :
\[CP-CP\left( \dfrac{10}{100} \right)\]

Applying the value of CP as 42000 in above formula we get,
The amount after deducting first rate of discount i.e. $D_1$ =10%
The amount after deducting first rate of discount \[=42000-42000\left( \dfrac{1}{10} \right)\]
\[\Rightarrow \] The amount after deducting first rate of discount = 42000-4200
\[\Rightarrow \] The amount after deducting the first rate of discount = 37800.
 Therefore, the amount left after providing $D_1$ is $CP_2$ = Rs.37800.


Now we proceed similarly to obtain the amount after applying second rate of discount that is to be provided on the $CP_2$ is,
\[C{{P}_{2}}-C{{P}_{2}}\left( \dfrac{10}{100} \right)\]

Substituting the values of $CP_2$ we have,
\[\begin{align}
  & C{{P}_{2}}-C{{P}_{2}}\left( \dfrac{10}{100} \right)=37800-37800\left( \dfrac{5}{100} \right) \\
 & \Rightarrow C{{P}_{2}}-C{{P}_{2}}\left( \dfrac{10}{100} \right)=37800-37800\left( \dfrac{1}{20} \right) \\
 & \Rightarrow C{{P}_{2}}-C{{P}_{2}}\left( \dfrac{10}{100} \right)=37800-1890 \\
 & \Rightarrow C{{P}_{2}}-C{{P}_{2}}\left( \dfrac{10}{100} \right)=35910 \\
\end{align}\]

Hence, we obtain the final amount after deducting all the interests $CP_2$ = Rs. 35910.

Now we calculate the amount of sales tax to be applied on the $CP_2$ using the formula,
\[CP\left( \dfrac{tax}{100} \right)\]

Substituting the value of CP and tax in above we get,
\[\begin{align}
  & CP\left( \dfrac{tax}{100} \right)=35910\left( \dfrac{8}{100} \right) \\
 & \Rightarrow CP\left( \dfrac{tax}{100} \right)=2872.80 \\
\end{align}\]

Therefore, the total amount of sales tax the customer has to pay is Rs. 2872.80

(ii)Now the total amount to be paid by the consumer including sales tax is $SP_1$ + tax
Substituting the values in above equation we get
$SP_1$ + tax = 35910+2872.80
\[\Rightarrow \] $SP_1$ + tax = 38782.80

Therefore, the total amount to be paid by the consumer for the computer set is = 38782.80

Note: The possibility of error in the question is deducting or applying both the discounts at the same time, which is wrong because adding both the discount percentages and then applying it together will lead to deduction of the selling price only once, But because discounts are applied twice so we need to deduct them from selling price separately.