If a shopkeeper sold one-third of his goods at a loss of 20%, then at what gain % should the remainder be sold to gain 25% on the whole transaction?

Let the total cost price of the goods be Rs. 300.
The overall target profit is 25% on the whole transaction.

Target Total Selling Price=300×(1+
100
25
​
)=Rs. 375
Step 1: Analyze the first part of the goods

One-third of goods cost
3
1
​
×300=Rs. 100.

These are sold at a 20% loss.

Selling Price of first part=100×(1−
100
20
​
)=Rs. 80
Step 2: Analyze the remaining part

Cost price of remaining goods =300−100=Rs. 200.

Required selling price for the remainder =375−80=Rs. 295.

Step 3: Calculate required gain percentage for remainder

Required Profit=295−200=Rs. 95
Gain %=(
200
95
​
)×100=47.5%