A merchant buys 80 articles, each at Rs. 40. He sells n of them at a profit of n% and the remaining at a profit of (100 – n)%. What is the minimum profit the merchant could have made on this trade?

minimum profit could have been 1580 rs.

merchent investement = 80*40 = 3200. Now given n qty are sold at (100+n)/100 cost & 80-n qty are sold at (200-n)/100 cost. add both & it gives us a quadratic eq for total cost i.e (2n^2 -180n+16000)/100 whose minima comes at 45 . Hope this explains everything.

if i want the profit to be minimum can i sell one article at 100% profit and the remaining articles at 0% profit so that i can get Rs 30 as my minimum profit

Can anyone clarify if there is a mistake

n=45, Minimum profit=770+810=1580

n=45; Minimum profit=770+810=1580

35 45 is giving the min as 1380 but why i am waiting for some elaboration