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Level 8Grade 8skill: discount_marked_price· 8 min read

Discounts and Marked Price

In short: A discount is a percentage of the marked price, so selling price = MP × (1 − rate/100). Two discounts never add: 20% then 10% multiplies to 0.80 × 0.90 = 0.72, a genuine 28% off, not 30%. Apply each percentage to the current price, and add sales tax last on the already-discounted amount.

From marked price to what you actually pay

Every price tag hides three numbers. The marked price (MP) is the sticker figure the shop prints. The discount is a percentage knocked off that figure. What is left, the amount you hand over, is the selling price (SP). The single rule that never fails: a discount is always a percentage of the marked price at the moment you apply it, so you must know which price you are taking the percentage of.

For one discount the shortcut is SP = MP × (1 − r/100). A 15% discount leaves 85% behind, so you multiply by 0.85 in one move instead of finding the discount and subtracting. The multiplier form matters even more once a second discount, or sales tax, enters the picture, because each new percentage acts on the current price, not the original sticker.

  1. Write down the marked price (MP) — the printed list price.
  2. Turn the discount into money: discount = (rate ÷ 100) × MP.
  3. Subtract, or take the shortcut SP = MP × (1 − rate/100).
  4. For a second discount, apply it to the reduced price, never the original MP.
  5. If tax or sales tax applies, add it last, calculated on the discounted price.

Why 20% then 10% is 28% off, not 30% Why it works

Single discount
SP = MP × (1 − r/100)

$1200 at 15% off → 1200 × 0.85 = $1020

Two discounts
Multiply the survivors: (1 − a/100)(1 − b/100)

20% then 10% → 0.80 × 0.90 = 0.72, so only 72% survives = 28% off

Net single rate
a + b − (a × b)/100

30% then 20% → 30 + 20 − (30 × 20)/100 = 50 − 6 = 44%

Discount + sales tax
sales tax rides on the discounted price and is added last

$5000, 20% off, 18% sales tax → 4000 × 1.18 = $4720

The second discount is smaller in dollars than the first, because it bites a price that has already shrunk. Add the rates and you double-count that overlap. For 20% and 10% the overlap is 2%, so the honest answer is 28%, and it is always a touch less than the sum. Whenever two percentages act one after another, multiply the fractions that remain; never add the percentages.

Worked examples

A jacket is marked $1200 and carries a 15% discount. What do you pay? = $1020
  1. 15% stays behind as 85%, so multiply by 0.85.
  2. SP = 1200 × 0.85 = 1020.
A watch marked $2500 has a festival offer of 20% off, and members get a further 10% off at the till. Find the final price and the single equivalent discount. = $1800, equivalent to a single 28% discount
  1. First discount: 2500 × 0.80 = 2000.
  2. Second discount acts on $2000, not $2500: 2000 × 0.90 = 1800.
  3. Total knocked off = 2500 − 1800 = 700, which is 700/2500 = 28% of the marked price.
  4. Check with the multiplier: 0.80 × 0.90 = 0.72, i.e. 28% off.
After a 15% discount a pair of shoes sells for $1020. What was the marked price? = $1200
  1. The $1020 represents the 85% that survived the discount.
  2. So 0.85 × MP = 1020, giving MP = 1020 ÷ 0.85.
  3. MP = 1200.
An appliance is marked $5000. The shop gives 20% off, then charges 18% sales tax on the discounted amount. What is the bill? = $4720
  1. Apply the discount first: 5000 × 0.80 = 4000.
  2. sales tax rides on the reduced price: 4000 × 1.18 = 4720.
  3. (Applying sales tax to the $5000 tag first would overcharge you — the discount must come off before tax is added.)
Shop A offers a flat 25% off a $4000 phone. Shop B offers 20% then a further 10%. Which is cheaper? = Shop B, at $2880 ($120 cheaper)
  1. Shop A: 4000 × 0.75 = 3000.
  2. Shop B: 4000 × 0.80 × 0.90 = 4000 × 0.72 = 2880.
  3. Shop B's stacked discount is worth 28%, beating the flat 25%, so it is cheaper by $120.

Common mistakes

Treating the percent sign as dollars

✗ On a $450 item at 10% off, writing 450 − 10 = $440.

The 10 is a percentage, not $10. Ten percent of 450 is 45, so you have subtracted far too little.

Fix: Convert first: 10% of 450 = (10/100) × 450 = 45, then SP = 450 − 45 = $405.

percent_as_whole

Stopping after the first discount

✗ On $2500 with 20% then 10%, computing 2500 × 0.80 = 2000 and calling $2000 the answer.

You applied only the first discount. There is still a 10% reduction to take off $2000, and the question asked for the final price, not the halfway price.

Fix: Carry the second discount through: 2000 × 0.90 = $1800. Always ask whether every discount — and the final subtraction — has actually been done.

partial_computation

Adding the two discount rates

✗ On $2500 with 20% then 10%, doing 20 + 10 = 30% and computing 2500 × 0.70 = $1750.

Percentages that act one after another do not add. The second 10% is taken from the reduced $2000, so it is worth less than 10% of the original. Adding double-counts the overlap and inflates the discount to 30% instead of the true 28%.

Fix: Multiply the survivors: 0.80 × 0.90 = 0.72, so SP = 2500 × 0.72 = $1800, a genuine 28% off.

wrong_operation

Taking both discounts off the original price

✗ On $2500 with 20% then 10%, computing 20% of 2500 = 500 and 10% of 2500 = 250, then 2500 − 500 − 250 = $1750.

The second discount was measured against the wrong base. Once the first discount lands, the price is $2000, so the 10% must come off $2000 (= $200), not off the original $2500 (= $250).

Fix: Update the base after each step: 2500 → 2000 (after 20%) → 1800 (after 10% of 2000). Final price $1800.

base_confusion

Practice: discounts and marked price

Work through multi-step problems on marked price, successive discounts and discount-plus-sales tax. Watch for the trap where adding two discount rates gives a tempting but wrong answer — multiply the surviving fractions instead, and keep track of which price each percentage acts on.

Related skills

First, make sure of

Frequently asked questions

Is a 20% then 10% discount the same as 30% off?

No. The second 10% is taken from the already-reduced price, so the discounts multiply rather than add: 0.80 × 0.90 = 0.72, which is a 28% discount. You save less than the 30% the two rates seem to promise.

How do I find the marked price when I know the selling price and the discount?

Divide, don't guess. If a 15% discount was given, the selling price is 85% of the marked price, so MP = SP ÷ 0.85. For SP = $1020 that gives MP = 1020 ÷ 0.85 = $1200.

Do you apply sales tax before or after the discount?

After. The discount comes off the marked price first, then sales tax is charged on that lower, discounted amount. On a $5000 item with 20% off and 18% sales tax: 5000 × 0.80 = 4000, then 4000 × 1.18 = $4720.

What is the fastest way to combine two successive discounts?

Multiply the fractions that survive each discount. For a% then b% the net multiplier is (1 − a/100)(1 − b/100); as a single rate it equals a + b − (a × b)/100. For 30% and 20% that is 50 − 6 = 44%.

Which is better, a flat 25% or 20% followed by another 10%?

The stacked 20% + 10% wins. It multiplies to 0.72, a 28% discount, which beats a flat 25%. On $4000 you pay $2880 instead of $3000.