Question

The price of a motorcycle is Rs 44880 including tax (under GST) at the rate of 18 % on its listed price. A buyer asks for a discount on the listed price so that after charging GST, the selling price of the motorcycle becomes equal to the listed price. Fin the discount in which the seller has to allow for the deal.

Answer 1

Hint: To solve this problem we first assume the price of the motorcycle excluding tax, and then we find the selling price of the motorcycle i.e. the listed price, and proceed with calculations. At the last find the discount using the discount formula.

Complete step by step solution:
Given, the price of a motorcycle including tax is Rs 44880.
Let the price of the motorcycle excluding tax = $Rs x$
And the GST tax on the motorcycle =$ 18 \%$
Since the price of the motorcycle tax + $18 \%$ of the price of the motorcycle = price of the motorcycle including tax.
i.e. $x + 18 \% \text{ of } x = Rs.44880$
Changing into equation form and solving for $x$
$
   \Rightarrow x + \dfrac{{18}}{{100}} \times x = 44880 \\
   \Rightarrow \dfrac{{118x}}{{100}} = 44880 \\
   \Rightarrow x = \dfrac{{44880 \times 100}}{{118}} = 38034 \\
 $
Now, according to the question, the selling price = listed price = Rs 44880
[Discount = Listed price – Selling price]
Now, discount on Rs 44880=$44880 – 38034$
= Rs 6846

$\therefore$ The discount amount on which the seller has to allow for the deal is Rs.6846.

Note:
To solve these types of questions we must know and understand the concept and formulae of how to find cost price, selling price, profit, loss, profit %, and loss %.
Discount: Discount is always given on list price or marked price, there is nothing to do with the cost price of an item in case of finding a discount on an item. Whereas profit and loss are always calculated on the cost price of an item. The term discount is mostly used by the seller not by the manufacturer. Do not confuse profit, loss, and discount.