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?

26%

We have,

Total number of items = 40

MP of the items is more than that of cost price is = 20%

The person sells 10 items at a discount = 10%

He sells 20 items at a discount = 15%

Now according to the question,

Let cost price of each items be Rs. 1

Cost price of 40 items = 1 × 40 = Rs. 40

MP of 40 items = 40 × (120/100) = Rs. 48

Selling price of 10 items = 10 × (120/100) × (90/100) = Rs. 10.8

Selling price of 20 items = 20 × (120/100) × (85/100) = Rs. 20.4

MP of the remaining 10 items = 10 × 120/100 = Rs. 12

Net profit = (12 + 20.4 + 10.8) - Rs. 40 = 43.2 - 40 = Rs. 3.2

If he gives discount Rs. 3.2 on Rs. 12 he gets neither profit nor loss.

Required discount = 3.2/12 × 100 = 26%