A person marks his 40 items at 20% of the cost price. He sells 10 items at a 10% discount and 20 items at a 15% discount on the marked price. What is the maximum discount (rounded off) he can offer on the remaining items if he still gets some profit?

Let the cost price of 40 items = 100C

Marked price of 40 items = $$\frac{120}{100}\times100C$$ = 120C

Marked price of 10 items = 30C

Discount on 10 items = 10%

Selling price of 10 items = $$\frac{90}{100}\times30C$$ = 27C

Marked price of 20 items = 60C

Discount on 20 items = 15%

Selling price of 20 items = $$\frac{85}{100}\times60C$$ = 51C

Selling price of 30 items = 78C

Selling price of the remaining 10 items if he gets neither profit nor loss = 22C

Let discount on the remaining 10 items = x

$$=$$> 30C - $$\frac{x}{100}$$ x 30C = 22C

$$=$$>  $$\frac{x}{100}$$ x 30C = 8C

$$=$$>  x = 26.66%

with 26.66% discount on remaining items he has no gain or loss

$$\therefore\ $$The maximum discount he can offer on the remaining items where he can still earn profit = 26%

Hence, the correct answer is Option B