Company C sells a line of 25 products with an average retail price of Rs 1,200. If none of these products sells for less than Rs 420 and exactly 10 of the products sell for less than Rs 1,000, then what is the greatest possible selling price of the most expensive product?

To calculate the maximum possible price of an item, take price of other items as minimum as possible.

Given that exactly 10 products sells for less than 1000 and no product should be less than 420.

So take the price of 10 items as 420 rs each (minimum possible price)

$$\therefore$$ Price of these 10 items will be 420 x 10 = 4200.

Now, remaining 14 items (except the high priced item) should be 1000 rs each (minimum possible price)

$$\therefore$$ Price of these 14 items will be 14 x 1000 = 14,000

And price of 24 items = 4,200 + 14,000 = 18,200 .....(1)

Given average retail price of 25 products = 1,200 (or) Total price of all items = 25 x 1,200 = 30,000

Now, the greatest possible price of the most expensive product is given by,

Total price of all items - minimum possible price of 24 items (i.e equation (1))

$$\Rightarrow$$ 30,000 - 18,200 = 11,800 

Hence, option D is the correct answer.