If half of the quantity of sugar in a bag was sold at a profit of 20%, a quarter of the quantity of sugar in the bag was sold at a profit of 16%, and the remaining sugar in the bag was sold at a profit of 24%, and the total profit obtained by selling all the sugar in the bag was ₹90, what was the cost price of the entire quantity of sugar in the bag?

₹450

Let the total quantity = 40

Half is sold at 20% profit means the selling price of half = 120% of 20 = 24

Quarter is sold at 16% profit means the selling price of quarter is = 116% of 10 = 11.6

Rest is sold at 24% profit means the selling price of rest is = 124% of 10 = 12.4

The total selling price = 24 + 11.6 + 12.4 = 48

Profit = 48 - 40 = 8

8x = 90

40x = 450