Question

A shop selling sewing machines offers a 3% discount on all cash purchases. What amount does a customer pay for a sewing machine (correct up to two decimal places) the price which is marked to Rs 650.

Answer 1

Hint: This question is from the topic of profit and loss. The concept used here is of discount. The key point to remember is that a discount is always calculated on the marked price, and once the discount is calculated, the selling price can be calculated by subtracting the discount from the marked price.
Formulae used:
\[{\text{discount}} = {\text{discount}}\% \; \times {\text{M}}{\text{.P}}{\text{.}}\]
\[{\text{S}}{\text{.P}}{\text{.}} = {\text{M}}{\text{.P}}{\text{.}} - {\text{discount}}\]
or \[{\text{S}}{\text{.P}}{\text{.}} = {\text{M}}{\text{.P}}{\text{.}} - {\text{discount}}\% \; \times {\text{M}}{\text{.P}}{\text{.}}\]
Where M.P. is the marked price, and S.P. is the selling price.

Complete step-by-step answer:
In the question, we are given the marked price and discount as shown below,
\[ \Rightarrow {\text{M}}{\text{.P}}{\text{.}} = 650\]
\[ \Rightarrow {\text{discount}}\% \; = 3\% \]
Now, according to the formula \[{\text{S}}{\text{.P}}{\text{.}} = {\text{M}}{\text{.P}}{\text{.}} - {\text{discount}}\% \; \times {\text{M}}{\text{.P}}{\text{.}}\], we have,
\[ \Rightarrow {\text{S}}{\text{.P}}{\text{.}} = 650 - 3\% \; \times 650\]
Now, calculating the required discount as shown below,
\[ \Rightarrow {\text{S}}{\text{.P}}{\text{.}} = 650 - \dfrac{3}{{100}} \times 650\]
While calculating the discount, keep in mind to calculate it up to two decimal places as shown below,
\[ \Rightarrow {\text{S}}{\text{.P}}{\text{.}} = 650 - 19.50\]
Now, subtracting the calculated discount from the marked price as shown below,
\[ \Rightarrow {\text{S}}{\text{.P}}{\text{.}} = 630.50\]
So, the correct answer is “S.P. = Rs.630.50”.

Note: We should know that the discount is always calculated on the marked price of an item. The profit percentage and loss percentage is always calculated over the cost price of an item. One must know the formula for selling price in the terms of marked price and percentage of discount as \[{\text{S}}{\text{.P}}{\text{.}} = {\text{M}}{\text{.P}}{\text{.}} - {\text{discount}}\% \; \times {\text{M}}{\text{.P}}{\text{.}}\]