A trader sells an article for `425 and loses 15%. At what price (in `) should he sell the article to earn 5% profit?

The correct answer is ₹525.

We are told the trader sells the article for ₹425 and loses 15%. This means the Selling Price (SP) is 15% less than the Cost Price (CP). We need to first find the CP, and then calculate the new SP that gives a 5% profit.

Step 1: Find the Cost Price (CP)

When there is a loss of 15%, the relationship between SP and CP is:

\mathrm{SP}=\mathrm{CP}\times \frac{100-\mathrm{Loss\%}}{100}

Substituting the known values:

425=\mathrm{CP}\times \frac{100-15}{100}

425=\mathrm{CP}\times \frac{85}{100}

Solving for CP:

\mathrm{CP}=\frac{425\times 100}{85}=\frac{42500}{85}=500

So the Cost Price = ₹500.

Step 2: Find the new Selling Price for a 5% Profit

When there is a profit of 5%, the new SP is calculated as:

\mathrm{New\; SP}=\mathrm{CP}\times \frac{100+\mathrm{Profit\%}}{100}

\mathrm{New\; SP}=500\times \frac{100+5}{100}

\mathrm{New\; SP}=500\times \frac{105}{100}=500\times 1.05=525

Conclusion: The trader should sell the article at ₹525 to earn a 5% profit. Notice that he must increase his selling price from ₹425 to ₹525 — an increase of ₹100 — to go from a 15% loss to a 5% gain.