A person bought n articles for ₹ d. He sold two articles at half their cost and the rest at a profit of ₹ 8 on each article. If the overall profit is ₹ 72, there the least possible value of n is

The person bought the n article, each at Rs. d.

In that, he sold two articles at Rs. $$\ \frac{\ d}{2}$$, which brings in Rs. d for him. 

Now, he sold the remaining n-2 articles at Rs. (d+8), which brings in Rs. (n-2)(d+8)

His total profit is Rs.72. This means, (n-2)(d+8)+d-nd = 72, or nd+8n-2d-16-nd = 72.

Hence 8n - 2d = 88, or 4n - d = 44

Now, d has to be greater than zero. Hence, the minimum value of n shall be 12 to make d as 4.