The ratio of the cost prices of articles X and Y is 3 : 7. A man earns a profit of 49% by selling X and loses 16% by selling Y. What is his gain/loss percentage in the entire transaction?7481

The correct option is Gain, 3.5%.

To find the overall gain or loss percentage, let us first assume convenient values for the cost prices of articles X and Y based on their given ratio of 3 : 7.
Let the cost price of article X ($C{P}_X$) be $300$ and the cost price of article Y ($C{P}_Y$) be $700$.
Therefore, the total cost price of both articles together is:
$\text{Total CP}=300+700=1000$

Next, we calculate the individual profit or loss on each article:
- The man earns a profit of 49% by selling article X:
$\text{Profit on X}=49\%\text{of}300=\frac{49}{100}\times 300=147$
- The man incurs a loss of 16% by selling article Y:
$\text{Loss on Y}=16\%\text{of}700=\frac{16}{100}\times 700=112$

Now, we find the net profit or loss in the entire transaction by subtracting the total loss from the total profit:
$\text{Net Result}=\text{Profit on X}-\text{Loss on Y}$
$\text{Net Result}=147-112=35$
Since the result is positive, it represents a net gain of 35.

Finally, we calculate the gain percentage on the total cost price of 1000:
$\text{Gain Percentage}=\left(\frac{\text{Net Gain}}{\text{Total CP}}\right)\times 100$
$\text{Gain Percentage}=\left(\frac{35}{1000}\right)\times 100=3.5\%$
Thus, the man earns a gain of 3.5% in the entire transaction.