Discounts appear on price tags, invoices, shopping apps and negotiated deals. The maths covers three standard situations: finding the sale price, finding the original price, and finding what percentage was discounted.
Finding the Sale Price After a Discount
Sale price = Original price × (1 − discount ÷ 100)
| Original price | Discount | Sale price |
|---|---|---|
| Rs 5,000 | 20% | 5,000 × 0.80 = Rs 4,000 |
| Rs 1,200 | 15% | 1,200 × 0.85 = Rs 1,020 |
| Rs 8,500 | 35% | 8,500 × 0.65 = Rs 5,525 |
Finding the Original Price
Original price = Sale price ÷ (1 − discount ÷ 100)
- Sale price Rs 3,500 after 30% off: 3,500 ÷ 0.70 = Rs 5,000
- Sale price Rs 765 after 15% off: 765 ÷ 0.85 = Rs 900
Finding the Discount Percentage
Discount % = ((Original − Sale) ÷ Original) × 100
- Was Rs 2,500, now Rs 1,875: (625 ÷ 2,500) × 100 = 25%
- Was Rs 4,000, now Rs 3,200: (800 ÷ 4,000) × 100 = 20%
Stacked (Sequential) Discounts
An extra 10% off a sale item already 40% off:
- Original: Rs 1,000
- After 40% off: Rs 600
- After another 10% off: Rs 600 × 0.90 = Rs 540
- Total saving: Rs 460 (46%), not 50%
Sequential discounts always give a smaller total saving than adding the percentages suggests, because the second discount applies to the already-reduced price.
The "Rs X off" vs "X% off" Comparison
When comparing a flat amount off versus a percentage:
- Rs 500 off a Rs 2,000 item = 25% off.
- Rs 500 off a Rs 4,000 item = 12.5% off.
The same absolute discount is proportionally smaller on a more expensive item. For quick calculations, use Discount Calculator. For percentage basics, see how to calculate percentages quickly.
GST on Discounted Prices
In Pakistan, GST typically applies to the price after the discount, not before. So a Rs 3,000 item with a 20% discount (sale price Rs 2,400) has GST applied to Rs 2,400. However, this depends on how the discount is structured — trade discounts versus promotional discounts can be treated differently for tax purposes. Confirm with FBR guidelines for your specific business situation. For calculating GST or VAT on any price, see how to calculate GST or VAT on a price.
Discount Calculator for Business Pricing
Wholesalers and distributors often apply trade discounts before calculating the selling price. A "25% off RRP" to a retailer means the retailer's cost is 75% of the recommended price, and they then apply their own markup for consumers. Discount Calculator handles all three problems: finding the sale price, extracting the pre-discount price, and calculating the discount percentage — useful at any stage of a supply chain.
