A person bought an article at 6 for Re. 1 and triple the previous amount at 5 for Re. 1. While selling 25% of the total articles are found damaged and unfit for selling. How many articles per Rs 23 should be sold so that there is an overall profit of 25%?

Hi Subhransu,
Scheme 1: 6 articles for rupees 1
Let the person buy x articles under this scheme. Therefore, the amount he spent to purchase x articles is (1/6)*x = (x/6) rupees.
Scheme 2: 5 articles for rupees 1:
It is given that the person buys thrice the articles in this scheme, which implies (3*x) = 3x articles are purchased under this scheme. Therefore, the amount he spent in this scheme to purchase 3x articles is (3x/5) rupees.
Hence, The total articles (together in scheme 1 and scheme 2) is (x+3x) = 4x articles, and the total amount spent by the person is {(x/6)+(3x/5)}= (23x/30) rupees.
Now, 25% of the articles are unfit for selling, which implies (4x*1/4) = x articles can't be sold. Hence, (4x-x) = 3x articles can be sold by the person to gain the desired profit.
To gain an overall profit of 25%, the overall selling price must be (125/100)*(23x/30) = (23x/24) rupees for 3x articles, which implies 1 rupee selling price for (3x/23x)*24 = (72/23) articles. Hence, 23 rupees were selling price for (72/23)*23 = 72 articles.
I hope this helps! Please let me know if you have any other queries,