Ravi bought some premium pens at Rs. 30 per pen and some regular pens at Rs. 15 per pen. He mixed all of them and marked each pen at 60% above the average cost price of all the pens bought. He sold the entire lot at 25% discount and made a profit of Rs. 180. Find the maximum number of pens bought by Ravi if he bought at least one pen of each type.

Let number of premium pens bought be ‘x’ and number of regular pens bought be ‘y’. So, total cost price of premium pens = 30 × x = Rs. ‘30x’ And total cost price of regular pens = 15 × y = Rs. ‘15y’ So, average cost price of all pens = Rs. (30x + 15y)/(x + y) Marked price of each pen = 1.6 × (30x + 15y)/(x + y) Selling price of each pen = 0.75 × 1.6 × (30x + 15y)/(x + y) Selling price of each pen = 1.2 × (30x + 15y)/(x + y) So, selling price of all the pens = 1.2 × (30x + 15y) = Rs. ‘36x + 18y’ ATQ; 36x + 18y - 180 = 30x + 15y Or, 6x + 3y = 180 So, 2x + y = 60 Since, x, y ≥ 1. minimum value of ‘x’ = 1 So, at ‘x’ = 1, ‘y’ = 58 and ‘x + y’ = 59 And at ‘x’ = 2, ‘y’ = 56 and x + y = 58 As we increase the value of ‘x’, the value of ‘x + y’ decreases. So, maximum value of ‘x + y’ = 59