The marked price of an article is ₹7500. A shopkeeper buys the article from a wholesaler at some discount and sells it to a consumer at the marked price. The sales are intra-state and the rate of GST is 12%. If the shopkeeper pays ₹90 as tax (under GST) to the State Government, find:

(i) the amount of discount.

(ii) the price inclusive of tax (under GST) of the article which the shopkeeper paid to the wholesaler.

Given:

Marked Price of the article = ₹7500

Let discount rate be $x$%

Cost price of article for shopkeeper = Marked Price - Discount

$= 7500 - \Big(\dfrac{x}{100}\times7500\Big) \\[1em] = ₹(7500 - 75x)$

As the sales are intra-state and the rate of GST is 12%, so GST comprises of 6% as CGST and 6% as SGST. wholesaler sells the article to shopkeeper for $7500 - 75x$, amount of GST collected by wholesaler from shopkeeper(or paid by shopkeeper)

CGST = 6% of $(7500 - 75x) = \Big(\dfrac{6}{100}\Big)\times(7500 - 75x) = ₹(450 - 4.5x)$

SGST = 6% of $(7500 - 75x) = \Big(\dfrac{6}{100}\Big)\times(7500 - 75x) = ₹(450 - 4.5x)$

∴ Amount of Input GST of shopkeeper:

Input CGST = $₹(450 - 4.5x)$
Input SGST = $₹(450 - 4.5x)$

Cost Price for Consumer = Marked Price of the article (as given in question) = ₹7500

The amount of GST collected by shopkeeper (or paid by consumer):

CGST = 6% of 7500 = $\dfrac{6}{100}\times$ 7500 = ₹450

SGST = 6% of 7500 = $\dfrac{6}{100}\times$ 7500 = ₹450

∴ Amount of Output GST of shopkeeper:

Output CGST = ₹450
Output SGST = ₹450

As the shopkeeper pays a tax (under GST) of ₹90 to the State Government:

Tax paid to state government by shopkeeper = Output SGST of shopkeeper - Input SGST of shopkeeper = ₹90

$\Rightarrow 450 - (450 - 4.5x) = 90 \\[0.5em] \Rightarrow 4.5x = 90 \\[0.5em] \Rightarrow x = \dfrac{90}{4.5} = 20\%$

(i) the amount of discount = Rate of discount x Marked Price

$= 20\% \text{ of Marked Price} \\[1em] = \Big(\dfrac{20}{100}\Big) \times 7500 \\[1em] = \bold{₹1500}$

(ii) the price inclusive of tax (under GST) of the article which the shopkeeper paid to the wholesaler = Cost price of article for shopkeeper + CGST paid by shopkeeper + SGST paid by shopkeeper

$= (7500 - 75x) + (450 - 4.5x) + (450 - 4.5x) \\[1em] = (7500 - (75\times20)) + (450 - (4.5\times20)) + (450 - (4.5\times20)) \\[1em] = 6000 + 360 + 360 = \bold{₹6720}$