Profit & Loss

Four prices appear in this topic: cost price (CP), selling price (SP), marked price (MP) and the discount. Keep them straight and the sums are one-liners.

• Gain = SP − CP, Loss = CP − SP
• Gain% = gain × 100 / CP — always on the cost price
• SP = CP × (100 + gain%)/100, so CP = SP × 100/(100 + gain%)
• SP = MP × (100 − discount%)/100 — discount is always on the marked price

The four question types:

1. Find gain or gain% from CP and SP.
2. Find CP from SP and gain% — divide by (100 + gain%), never subtract the percentage from the SP.
3. Two selling prices, one at a loss of a% and one at a gain of b%. The gap between them is (a + b)% of the CP — the percentages add, because one is below cost and the other above.
4. Markup then discount. Take CP = 100, compute MP, then apply the discount to MP. The answer is not markup − discount, because the two percentages sit on different bases.

The single most common mistake is computing profit percent on the selling price. Before you divide, ask: "percent of what?" The answer in this topic is the cost price, every single time.

Gain% = (SP − CP) × 100 / CP · CP = SP × 100/(100 + g%) · SP = MP × (100 − d%)/100 · loss a% and gain b% differ by (a+b)% of CP

By selling an article for ₹1,240 a shopkeeper gains 24%. Find the cost price. → SP is 124% of CP, so CP = 1240 × 100/124 = ₹1,000. Sanity check: 24% of ₹1,000 is ₹240, and ₹1,000 + ₹240 = ₹1,240. The tempting wrong move — taking 24% off ₹1,240 to get ₹942.40 — fails this check.