A merchant blends 350 kg of tea costing sh. 84 per kg with 140 kg of tea costing sh. 105 per kg. At what price must he sell the mixture to gain [tex]$25\%$[/tex]?

Sure, let's solve this step-by-step.

1. Calculate the total cost and weight of the blended tea:

- Tea 1:
- Weight = 350 kg
- Cost per kg = sh. 84
- Total cost of Tea 1 = 350 kg sh. 84/kg = sh. 29400

- Tea 2:
- Weight = 140 kg
- Cost per kg = sh. 105
- Total cost of Tea 2 = 140 kg sh. 105/kg = sh. 14700

2. Find the total weight of the mixture:

- Total weight = Weight of Tea 1 + Weight of Tea 2
- Total weight = 350 kg + 140 kg = 490 kg

3. Find the total cost of the mixture:

- Total cost = Total cost of Tea 1 + Total cost of Tea 2
- Total cost = sh. 29400 + sh. 14700 = sh. 44100

4. Calculate the cost per kg of the mixture without gain:

- Cost per kg without gain = Total cost / Total weight
- Cost per kg without gain = sh. 44100 / 490 kg = sh. 90.0 per kg

5. Determine the selling price per kg to achieve a 25% gain:

- Selling price per kg with gain = Cost per kg without gain (1 + Desired gain percentage/100)
- Selling price per kg with gain = sh. 90.0 (1 + 25/100)
- Selling price per kg with gain = sh. 90.0 * 1.25 = sh. 112.5

So, to gain a 25% profit, the merchant must sell the tea mixture at sh. 112.5 per kg.