Mental math tricks for discounts and profit/loss

Discount and profit/loss questions are, at their core, just percentage-of-a-number problems dressed up in shopping-cart language. If you're comfortable building percentages from 10%/1% blocks, this entire topic becomes fast pattern recognition rather than fresh calculation each time.

Discounts: subtract a percentage from the marked price

A discount reduces the marked price (MP) to a selling price (SP):

The fast approach: find the discount amount using percentage building blocks, then subtract — don't compute the selling price percentage directly unless the discount is a clean number like 50% or 25%.

Worked example: 15% off ₹840

• 10% of 840 = 84
• 5% of 840 = half of 84 = 42
• 15% = 84 + 42 = 126

Successive discounts: don't just add the percentages

A common trap: "20% off, then an extra 10% off" is not a 30% discount. Each discount applies to the already-reduced price, so you multiply the remaining fractions:

So the combined effect is a 28% discount, not 30% — always slightly less than simply adding the two percentages, because the second discount is applied to a smaller base.

Worked example: successive discounts of 20% and 10% on ₹2,500

• After 20% off: 2,500 × 0.8 = 2,000
• After a further 10% off: 2,000 × 0.9 = 1,800

Quick shortcut for two successive discounts

For two discounts a% and b%, the single-equivalent-discount formula is:

For 20% and 10%: 20 + 10 − (20×10/100) = 30 − 2 = 28%, matching the result above without multiplying fractions at all.

Profit and loss: percentage of the cost price

Profit or loss percentage is always calculated on the cost price (CP), not the selling price — a frequent source of exam mistakes.

The mental shortcut works the same way as discounts, just in reverse: instead of subtracting a percentage from MP, you're adding a percentage to CP to reach SP.

Worked example: bought at ₹640, sold at 25% profit

• 10% of 640 = 64
• 25% = 64 × 2.5 = 160 (using 25% = 10% × 2.5, or equivalently a quarter of 640)

Working backward: given SP and profit%, find CP

This direction trips people up because it's tempting to just subtract the percentage from SP — but profit% is defined on CP, not SP, so you need to divide, not subtract a flat percentage of SP.

For a loss, flip the sign: CP = SP × 100 / (100 − Loss%).

Worked example: sold at ₹690 for a 15% loss — find CP

For exam purposes, questions are usually designed so this division comes out clean — if it doesn't, double-check whether the percentage was meant to apply to CP or SP.

Marked price vs. cost price: don't mix them up

A classic multi-step question gives a discount off the marked price and a profit over the cost price in the same problem. Keep the two percentages on separate bases:

Solve for whichever quantity is missing by working through this chain one step at a time rather than trying to combine both percentages into one shortcut — that's where most errors happen.

Where this actually helps

Discount and profit/loss questions are a staple of bank exam and competitive exam quant sections, often combined with successive-percentage or multi-step word problems. Recognizing the pattern quickly — and knowing which base each percentage applies to — is usually worth more time saved than raw calculation speed.