How Discounts Are Calculated — Single, Stacked, and Why 20+10 ≠ 30%

“50% + 20% OFF!” screams the banner. You might think that’s 70% off. It’s not. It’s 60%. Understanding discount math can save you from disappointment — and help you spot genuinely good deals.

Single discount

Sale Price = Original × (1 − Discount/100)
Savings = Original × (Discount/100)

₹2,000 shirt at 30% off:

Sale Price = ₹2,000 × 0.70 = ₹1,400
You save: ₹600

Stacked (successive) discounts

When a store offers “50% + 20% extra” — the second discount applies to the already-reduced price, not the original.

After first:  ₹2,000 × 0.50 = ₹1,000
After second: ₹1,000 × 0.80 = ₹800

Effective discount: (₹2,000 − ₹800) / ₹2,000 = 60%, not 70%.

The general formula for stacked discounts

Effective % = (1 − (1 − D1/100) × (1 − D2/100)) × 100

For 50% + 20%:

= (1 − 0.50 × 0.80) × 100
= (1 − 0.40) × 100
= 60%

Why the order doesn’t matter

Mathematically, 50% then 20% gives the same result as 20% then 50%:

50% then 20%: 0.50 × 0.80 = 0.40 (60% off)
20% then 50%: 0.80 × 0.50 = 0.40 (60% off)

Multiplication is commutative. The final price is always the same regardless of which discount is applied first.

Finding original price from sale price

If an item costs ₹800 “after 20% off” — what was the original?

Original = Sale Price / (1 − Discount/100)
         = ₹800 / 0.80
         = ₹1,000

Real-world applications

• Credit card “instant discount + bank offer” — these stack
• Coupon codes on top of sale prices
• GST-inclusive vs pre-discount pricing confusion
• “Up to 70% off” — the effective discount on your item is usually much lower

Calculate exact savings with the OurDailyCalc discount calculator — it handles stacked discounts and shows effective percentage.

TL;DR

• Single discount: Original × (1 − rate%)
• Stacked: second discount applies to reduced price, not original
• 50% + 20% = 60% effective (not 70%)
• Order of discounts doesn’t matter mathematically