A 15% discount followed by a further 10% discount reduces the original price by a total of 23.5%. This is because the second discount is deducted from the already reduced amount. Simply adding the two percentages would imply a different rule: that both apply to the original price.
Before purchasing, check the basis for the discounts and whether they can be combined. The calculation follows only the specified conditions; the mere existence of two coupons does not imply that both can be applied to a single order.
Calculate using the remaining portion of the price
After a 15% discount, you pay 85% of the price; after a ten per cent discount, you pay 90%. The multipliers are 0.85 and 0.90.
In general, if the original price is A, and the two sequential discounts are p and q per cent, the final price is A × (1 − p/100) × (1 − q/100). The total discount in per cent is 100 × [1 − (1 − p/100) × (1 − q/100)]. The multiplier derived from the discount is also presented in the OpenStax chapter on discounts. The following examples are our own calculations, using assumed prices.
For a 24 000 Ft product, the first discount of 15% is 24 000 × 0.15 = 3600 Ft. After the first step, 20 400 Ft remains. The further 10% of this is 2040 Ft, so the final price is 18 360 Ft. The total saving is 5640 Ft, which is 5640 / 24 000 × 100 = 23.5%.
If you incorrectly deducted 25%, you would get a final price of 18 000 Ft. The 360 Ft difference arises because you would have calculated a discount on the 3600 Ft already waived from the original price in the second step.
When does the order matter?
For two purely percentage-based discounts applied to the current price, the order is interchangeable in exact calculation: 0.85 × 0.90 is the same as 0.90 × 0.85. The intermediate amounts differ, but the final sum is identical. With step-by-step currency rounding, a small discrepancy may arise, so also consider the rounding order of the actual till calculation.
With a fixed-amount coupon, the order can significantly alter the result. For the same assumed 24 000 Ft product, let there be a 2000 Ft coupon and a 15% discount.
| Order of application | Calculation | Amount payable |
|---|---|---|
| First 15%, then 2000 Ft | 24 000 × 0.85 − 2000 | 18 400 Ft |
| First 2000 Ft, then 15% | 22 000 × 0.85 | 18 700 Ft |
In the second case, the base for the percentage discount is 2000 Ft lower. 15% of this is the 300 Ft difference between the two results. To understand the difference seen at the till, you must compare the coupon conditions with the actual order.
Product price and order total
If the 18 360 Ft discounted product in the example incurs a further 1490 Ft for shipping, the total expenditure is 19 850 Ft. Assume another offer for the same product at 19 500 Ft, where shipping is included in the price. The latter represents 350 Ft less in total expenditure. Thus, a larger advertised discount alone does not rank the offers.
If the coupon applies only to part of the basket, first split the items into eligible and excluded products. Apply the product of the two discounts only to the subtotal that receives both. Add the remaining items at their applicable discount or full price, then calculate shipping. For items with differing eligibility, applying a single discount percentage to the entire basket may yield an incorrect final sum.
In the discount calculator, you can also calculate the effect of sequential percentage discounts. Check the fixed coupon and the separate shipping item according to the assumed order; do not expect a purely percentage-based calculation to handle these automatically.
When working backwards, dividing 18 360 Ft by 0.85 × 0.90 recovers the starting price of 24 000 Ft. However, with a hundred per cent discount, the remaining multiplier is zero, so the original price cannot be restored from this single result. For comparison, always retain the original price, the order of discounts, and any separately charged items.
What coupon size fits within the budget?
Let us reverse the question with a new example. The assumed base price of the product is 32 000 Ft, the first discount is 20%, and shipping is 1490 Ft throughout. A maximum of 24 000 Ft is available for the total expenditure. The second, percentage-based coupon applies to the already discounted product price and does not reduce shipping.
After the first discount, the product price is 32 000 × 0.80 = 25 600 Ft. After shipping, 22 510 Ft remains from the budget for the product (24 000 − 1490). If q is the percentage value of the coupon, this must be satisfied:
25 600 × (1 − q/100) ≤ 22 510.
The permitted price multiplier is at most 22 510 / 25 600 = 0.879296875. The required discount is therefore at least 1 − 0.879296875 = 0.120703125, i.e. 12.0703125%.
If only whole percentage coupons can be chosen, 12% is insufficient. With this, the total expenditure is 25 600 × 0.88 + 1490 = 24 018 Ft, which exceeds the budget by 18 Ft. The 13% variant is 25 600 × 0.87 + 1490 = 23 762 Ft, leaving 238 Ft.
When calculating the limit, retain the exact value: rounding 12.0703125% to 12% first would lose the condition of 'at most 24 000 Ft'. Round in the direction that satisfies the condition for the available coupon steps, then recalculate the total amount.
This derivation applies to the fixed 1490 Ft shipping and the coupon applicable to the discounted product. Check the minimum basket and shipping price threshold on the amount before or after the coupon, according to the shop's rules.
When the coupon increases the amount payable
Modify the shipping rule from the previous example: the post-coupon product price must be at least 25 000 Ft for free shipping; below this, the fee is 1490 Ft. An order of 25 600 Ft without a coupon thus totals 25 600 Ft.
With a 5% coupon, the product price drops to 24 320 Ft, so shipping becomes payable. The final sum is 24 320 + 1490 = 25 810 Ft, meaning the use of the coupon causes an excess of 210 Ft. In the fee-paying range, the discount must waive more than 1490 Ft for the order to actually be cheaper: q > 1490 / 25 600 × 100 = 5.8203125%. At six per cent, the final sum is 25 554 Ft, and the actual saving is 46 Ft.
At the price threshold, calculate the two payment branches separately. The total expenditure does not necessarily decrease continuously with the discount; it may jump at once due to the shipping condition.
Final knowledge test
Choose one answer for each question. Each correct answer earns 1 point; an incorrect answer, a skipped question or more than one selected answer earns 0 points. You can score 0–3 points in total. Read the solutions after answering.
1. From 24 000 Ft, first 15%, then 10% is deducted from the reduced price. What is the final price and the combined discount?
- A) 18 360 Ft and 23.5%.
- B) 20 400 Ft and 15%.
- C) 18 000 Ft and 25%.
2. A 25 600 Ft product price incurs 1490 Ft shipping throughout. You would pay at most 24 000 Ft. You can choose a whole percentage product coupon. What is the smallest sufficient coupon?
- A) 12%.
- B) 10%.
- C) 13%.
3. 25 600 Ft is the pre-coupon product price. Free shipping is only available for a post-coupon product price of at least 25 000 Ft; below this, the fee is 1490 Ft. What does the 5% coupon cause?
- A) The total expenditure will always be at least 5% lower.
- B) The total expenditure will be 24 320 Ft.
- C) The total expenditure will be 25 810 Ft, 210 Ft more.
Solutions and scoring
1. A. The remaining multiplier is 0.85 × 0.90 = 0.765. The final price is 24 000 × 0.765 = 18 360 Ft; 1 − 0.765 = 23.5% is the discount. For revision: Calculate using the remaining portion of the price.
2. C. The exact limit is 12.0703125%. With twelve per cent, the total expenditure is 24 018 Ft; with 13%, it is 23 762 Ft, so you must choose upwards for whole steps. For revision: What coupon size fits within the budget?.
3. C. The product drops to 24 320 Ft, triggering the shipping fee. The total amount is 24 320 + 1490 = 25 810 Ft. For revision: When the coupon increases the amount payable.
Each correct answer is worth 1 point; an incorrect or omitted answer is worth 0 points. The total score can be 0–3.
- 0 points: work through the sections indicated in the three solutions again, and write down the initial conditions of the examples.
- 1 point: derive the correct answer for the two missed questions; separately note which condition or calculation step was omitted.
- 2 points: return to the section linked to the single missed question, then verify the result again by changing one input.
- 3 points: you correctly applied the three relationships in this task set. Try one of the article's checks with your own data, recording the conditions and units as well.
Translated and adapted from the Hungarian article: Hungarian original.