a shopkeeper mixes 60 kg of sugar worth rs. 30 per kg with 90 kg of sugar worth rs. 40 per kg. at what rate he must sell the mixture to gain 20%?

Shopkeeper's Sugar Mixture Profit Calculation A shopkeeper mixes 60 kg of sugar at Rs. 30/kg with 90 kg at Rs. 40/kg, totaling 150 kg. To gain 20% profit, first calculate the total cost price (CP), then determine the selling price (SP) per kg needed. Step-by-Step Solution

1. Calculate Total Cost Price (CP):
   • Cost of first sugar: 60×30=180060\times 30=180060×30=1800 Rs.
   • Cost of second sugar: 90×40=360090\times 40=360090×40=3600 Rs.
   • Total CP: 1800+3600=54001800+3600=54001800+3600=5400 Rs. for 150 kg.
   • CP per kg: 5400150=36\frac{5400}{150}=361505400​=36 Rs/kg.
2. Determine Selling Price for 20% Profit:
   • 20% profit on CP means SP = CP × 1.20.
   • SP per kg: 36×1.20=43.236\times 1.20=43.236×1.20=43.2 Rs/kg.
3. Verify Profit:
   • Profit per kg: 43.2−36=7.243.2-36=7.243.2−36=7.2 Rs.
   • Profit %: 7.236×100=20%\frac{7.2}{36}\times 100=20%367.2​×100=20%.

Final Answer:
The shopkeeper must sell the mixture at Rs. 43.20 per kg to gain 20%.

| Description       | Amount (Rs.) |
|-------------------|--------------|
| Total CP (150 kg) | 5400        |
| Required SP       | 6480        |
| SP per kg         | 43.20       |

TL;DR: Sell at Rs. 43.20/kg for 20% profit on Rs. 5400 total cost.