The ratio of the cost prices of articles X and Y is 1:2. A man earns a profit of 12% by selling X and incurs a loss of 36% by selling Y. What is his overall gain or loss percentage in the entire transaction?

The correct option is Loss, 20%.

Let us break down the solution step-by-step to understand why this is the correct answer.

Step 1: Define the Cost Prices
The ratio of the cost prices of articles X and Y is given as 1:2.
To make calculations simple, let us assume:
Cost Price of article X (CP_X) = $100$
Cost Price of article Y (CP_Y) = $200$

Therefore, the total cost price of both articles together is:
Total CP = CP_X + CP_Y = $100+200=300$

Step 2: Calculate the Selling Prices
For article X, a profit of 12% is earned.
Profit on X = 12% of CP_X = $\frac{12}{100}\times 100=12$
Selling Price of X (SP_X) = CP_X + Profit =

For article Y, a loss of 36% is incurred.
Loss on Y = 36% of CP_Y = $\frac{36}{100}\times 200=72$
Selling Price of Y (SP_Y) = CP_Y - Loss = $200-72=128$

Step 3: Calculate the Total Selling Price and Overall Net Profit/Loss
Total Selling Price (Total SP) = SP_X + SP_Y = $112+128=240$

Since the Total SP (240) is less than the Total CP (300), there is an overall loss:
Overall Loss = Total CP - Total SP = $300-240=60$

Step 4: Calculate the Overall Loss Percentage
The overall loss percentage is calculated as:
Overall Loss % = $\left(\frac{\text{Overall Loss}}{\text{Total CP}}\right)\times 100$

Substituting the values:
Overall Loss % = $\left(\frac{60}{300}\right)\times 100=20\%$

Thus, the man incurs an overall Loss of 20% in the entire transaction.