A dealer buys two articles X and Y for ₹800 each. He marks each of them at the same price. He sells X by giving two successive discounts of 45% and 73% and still earns ₹523 as profit. If he sells Y at a single discount of 89%, then what is the profit percentage on Y?

Correct option is D

Given
Cost Price of X = ₹800
Cost Price of Y = ₹800
Marked Prices are the same for both.
Discounts on X = 45% and 73%
Profit on X = ₹523
Discount on Y = 89%
Formula Used
Selling Price = Marked Price $$\times (1 - \frac{Discount_1}{100}) \times (1 - \frac{Discount_2}{100})$$​​
Selling Price = Cost Price + Profit
Solution
Selling Price of X = 800 + 523 = 1323
Let Marked Price be M.
​$$M \times (1 - 0.45) \times (1 - 0.73) = 1323 \\\ \\M \times 0.55 \times 0.27 = 1323\\\ \\M \times \frac{55}{100} \times \frac{27}{100} = 1323\\\ \\M \times \frac{1485}{10000} = 1323 \Rightarrow M = \frac{13230000}{1485} = 8909.09...\\\ \\M = \frac{1323 \times 100 \times 100}{55 \times 27} = \frac{13230000}{1485} = \frac{98000}{11}\\\ \\$$​​
Selling Price of Y at 89% discount = $$M \times (1 - 0.89) = 0.11 \times M$$​​
Selling Price of Y = $$\frac{11}{100} \times \frac{98000}{11} = 980$$​​
Profit on Y = 980 - 800 = 180
Profit Percentage on Y = $$\frac{180}{800} \times 100 = \frac{18}{8} \times 10 = 22.5\%$$​​
Final Answer
So the correct answer is (d)
Exam Hall Method: