On the sale of a certain item a shopkeeper offered two successive discounts such that in percentage terms the second discount was only $$\frac{1}{n}$$​th of the first. If the overall discount was p% of the marked price of the item, then the selling price of the item after applying only the first discount was Rs y and the marked price of the item was Rs x.

Which one of the following is correct in respect of the Question and the Statements given below?

Statement 1: The values of n, p, y and x are respectively given as 3, 15.52, 8900 and 10000.

Statement 2: The values of n, p, y and x are respectively given as 4, 21.69, 12730 and 15500.

Correct option is C

Given:

​$$D_2 = \frac{1}{n} D_1$$​​

Effective discount D = $$p\%$$​​

Marked price $$\times D_1 = y$$  

x = Marked rice

y = Selling price after 1st discount

Formula Used:

For finding $$D_1$$​:

​$$D_1 = \frac{MP - SP}{MP} \times 100$$​​

For the overall effective discount:

​$$p = \left( - D_1 - D_2 + \frac{D_1 \times D_2}{100}\right)\%$$​​​

Solution:

For Statement 1: The values of n, p, y and x are respectively given as 3, 15.52, 8900 and 10000.

n = 3, p = 15.52, y = 8900, x = 10000

Discount (MP - SP) = 1100, MP = 10000, and SP 8900

​$$D_1 = \frac{10000 - 8900}{10000} \times 100 = \frac{1100}{10000} \times 100 = 11\%$$​​

​$$D_2 = \frac{1}{n} D_1 = \frac{1}{3} \times 11 = \frac{11}{3} \approx 3.67\%$$​​

Calculating the effective discount:

​$$p = - 11 - 3.67 + \frac{11 \times 3.67}{100} = -11 - 3.67 + 0.4037 = -14.26\% \ne15.52\%$$​​

This statement does not matches the given effective discount, so Statement 1 is incorrect.

For Statement 2: The values of n, p, y and x are respectively given as 4, 21.69, 12730 and 15500.

n = 4, p = 21.69, y = 12730, x = 15500

$$D_1 = 15500 - 12730 = 2770$$​ 

​$$D_1\% = \frac{2770}{15500} \times 100 = 17.87096\%$$​​

​$$D_2 = \frac{ 17.87096}{4} = 4.46774\%$$​​

Calculating the overall discount:

​$$p = -17.87096 - 4.46774 + \frac{17.87096 \times 4.46774}{100} = -17.87096 - 4.4677 + 0.79842 = -21.54024 \ne - 21.69\%$$​​

This statement does not  match the given effective discount of 21.69%. Therefore, Statement 2 is incorrect.

Thus, the correct option is (c) Neither of the two statements is feasible.