Q.A shopkeeper marks his goods 40% above the cost price and then allows a discount of 25% on the marked price. Find his profit or loss percentage.

Take the cost price as 100, build up the marked price using the 40% mark-up, then apply the 25% discount to reach the selling price and compare with the cost price.

This problem chains all three prices, so take a convenient cost price of $CP=₹100$.

Step 1 — Find the marked price (40% above cost).

Step 2 — Apply the 25% discount on the marked price.

Step 3 — Compare the selling price with the cost price. Since $SP=₹105>CP=₹100$, there is a profit:

$\text{Profit}\%=\frac{SP-CP}{CP}\times100=\frac{105-100}{100}\times100=5\%.$ …

A common mistake is to think a 40% mark-up followed by a 25% discount cancels to a 15% gain. The two percentages sit on different bases (mark-up on CP, discount on MP), so they mus …