A shopkeeper sold first unit of an article to Aria at 20% discount and the second unit of the same article at 40% discount. If the shopkeeper earned an overall profit of 5%, the marked price of the article was what percent of the cost price of the article ?

Let the cost price of each article = Rs. $$100x$$

=> C.P. of both articles = $$2 \times 100x = 200x$$

=> Selling price = $$\frac{105}{100} \times 200x = 210x$$ ------------------Eqn(1)

Let the marked price = Rs. $$100y$$

Selling price of 1st article after 20% discount = $$\frac{80}{100} \times 100y = 80y$$

Selling price of 2nd article after 40% discount = $$\frac{60}{100} \times 100y = 60y$$

=> Total selling price = $$80y + 60y = 140y$$ --------------------Eqn(2)

Comparing eqns(1) & (2), we get :

=> $$210x = 140y$$

=> $$\frac{y}{x} = \frac{210}{140} = \frac{3}{2}$$

$$\therefore$$ Required % = $$\frac{3}{2} \times 100 = 150 \%$$