Question

A shopkeeper sells an article for $Rs.1770$ with a GST of $18\%$. A customer who is willing to buy this article, asks the shopkeeper to reduce the price of the article so that he pays only $Rs.1888$ including GST. If the shopkeeper agrees to this,  How much reduction will the shopkeeper give?

Answer 1

Hint: The Goods and Services Tax (GST) is collected when a consumer buys products or receives a service. GST is calculated on the Original cost.

GST Amount = Original cost $\times \dfrac{\text{GST%}}{100}$ and

Overall Cost (Selling price) = Original cost + GST Amount 

The selling price of the article by the shopkeeper is equal to the cost price of the same article for the customer who’s buying it.  Using this logic, we will find the amount of reduction in the original price given by the shopkeeper.

Complete step by step answer:

Given, The original cost of the article is $Rs.1770$ and

The GST on the article is $18\%$. This $18\%$ GST is calculated on the original cost of the article.

Required Cost price for the customer to buy the article is $Rs.1888$ Including GST.

The Selling price of the article will be equal to (Original cost + GST Amount)

Selling price = $Rs. 1770 + \left(\dfrac{18}{100} \times 1770 \right)$

Selling price = $Rs. 1770+318.6$

Therefore, the overall price of the article = $Rs.2088.60$. But we don’t require this price here.

To get the article at the required cost price, the shopkeeper needs to reduce the original cost to less than $Rs. 1770$.

Let the amount Reduced be $P$.

Then the original cost of the article becomes $Rs. 1770-P$

According to the given condition, GST will be the same as $18\%$ on the reduced price.

$\Rightarrow $ Overall cost after reducing the price = $(1770-P) + \dfrac{18}{100} \times (1770-P) $ 

The Reduced selling price of the article by the shopkeeper is equal to the cost price of the same article for the customer. So, we get

Cost price = Overall cost after reducing the price 

$1888 = (1770-P) + \dfrac{18}{100} \times (1770-P) $ 

Solving for $P$

$1888 = (1770-P) \times \left( 1+\dfrac{18}{100} \right)$

$\Rightarrow 1888 = (1770-P) \times \left(\dfrac{118}{100}\right)$

On simplification,

$ 1888 \times \dfrac{100}{118} = (1770-P)$

$\Rightarrow 16 \times 100 = (1770 -P)$

On further simplification, we get

$P= 1770 - 1600$

$\therefore P= 170$

Therefore the amount of the cost reduced by the shopkeeper is $Rs. 170$, so that the customer will get the article at $Rs.1888$ including GST.

Note: 

• Students need to take care while calculating the GST. The GST is always calculated w.r.t. the original cost. If the Original cost is reduced, GST should be calculated w.r.t. the reduced cost. Otherwise, it leads to incorrect prices.

• If we are buying articles, we can see the Maximum Retail Price (MRP) on the labels. Note that this MRP includes all the taxes including GST.