A shopkeeper marked an article at ₹ 2000. The rate of GST on the article is 18%. The customer has only ₹ 1888 with him and he requests the shopkeeper to reduce the price so that he can buy the article at ₹ 1888 including GST. What percent discount must the shopkeeper give to do so?
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Given,
Marked price of the article = ₹ 2000
Rate of GST = 18%
Amount available with the customer = ₹ 1888 (including GST)
Let the reduced price of the article be ₹ $x$.
⇒ $x + 18% \text{ of } x = 1888$
$$\begin{aligned}\Rightarrow x + \frac{18}{100} \times x = 1888 \\[1em] \Rightarrow x\Big(1 + \frac{18}{100}\Big) = 1888 \\[1em] \Rightarrow x \times \frac{118}{100} = 1888 \\[1em] \Rightarrow x = \frac{1888 \times 100}{118} \\[1em] \Rightarrow x = 1600.\end{aligned}$$
Reduced price of the article = ₹ 1,600
Reduction in price = ₹ 2000 − ₹ 1600 = ₹ 400
By formula,
Discount % = $\frac{\text{Reduction in price}}{\text{Marked price}} \times 100$
= $\frac{400}{2000} \times 100$
= 20%.
Hence, the shopkeeper must give a discount of 20%.