A seller decreased the selling price of each item from ₹5,000 to ₹4,680, by which his loss percentage increased by 4%. If he has to get 4% profit, then the selling price of the item should be:

The correct option is ₹8,320.

Let the cost price of each item be $CP$.

Initially, the selling price ($S{P}_1$) of each item is ₹5,000.

The new selling price ($S{P}_2$) after decreasing the price is ₹4,680.

The decrease in selling price is given by:

$\text{Decrease in}SP=S{P}_1-S{P}_2$

$\text{Decrease in}SP=5000-4680=\text{₹}320$

According to the question, decreasing the selling price by ₹320 causes the loss percentage to increase by 4%.

Since loss percentage is always calculated on the cost price ($CP$), this increase of 4% in loss percentage corresponds directly to the change in selling price of ₹320.

$4\%\text{of}CP=320$

Now, we can find the total cost price ($CP$):

$\frac{4}{100}\times CP=320$

$CP=\frac{320\times 100}{4}$

$CP=80\times 100=\text{₹}\mathrm{8,000}$

So, the cost price of each item is ₹8,000.

Now, we need to find the selling price ($S{P}_{\text{new}}$) required to achieve a profit of 4%.

$S{P}_{\text{new}}=CP+(4\%\text{of}CP)$

We already know that 4% of $CP$ is ₹320.

$S{P}_{\text{new}}=8000+320=\text{₹}\mathrm{8,320}$

Therefore, to earn a profit of 4%, the selling price of the item should be ₹8,320.