Q.An article is sold for ₹360 at a loss of 10%. Find its cost price.

A loss of 10% means the selling price is 90% of the cost price, so the cost price is recovered by dividing the selling price by 0.90.

$CP=\dfrac{360}{1-0.10}=\dfrac{360}{0.90}=₹400$.

Here $SP=₹360$ and the sale is at a loss of $10\%$ on the cost price, which is unknown.

Step 1 — Relate SP to CP. A loss of $10\%$ means the selling price is $(100-10)=90\%$ of the cost price:

Step 2 — Solve for CP.

Check (independent verification). Loss $=CP-SP=400-360=₹40$, and $\dfrac{40}{400}\times100=10\%$, which matches the stated loss.

'$CP=100$' method: at a 10% loss, when CP is 100 the SP is 90. Here SP is ₹360, so the scale factor is $\dfrac{360}{90}=4$; hence $CP=100\times4=₹400$.

A frequent slip is taking 10% of the selling price and adding it back — $360+36=₹396$ — which is wrong because the loss percentage is on the cost price, not the selling price. Divide by 0.90 rather than adding 10% of SP.