Discount Formula - Definition, Steps, Examples

Key Points

• The discount formula is $D = \text{MP} - \text{SP}$, the marked price minus the selling price.

• The discount percentage is $d = \frac{D}{\text{MP}} \times 100$, always taken on the marked price and never on the selling price.

• Rearranged, the selling price after a discount is $\text{SP} = \text{MP}\left(1 - \frac{d}{100}\right)$.

• Two successive discounts do not add, so 20 per cent followed by 10 per cent gives a single equivalent discount of 28 per cent, not 30.

• The marked price is the list or sticker price before reduction, which is the base every discount percentage is measured against.

What Is the Discount Formula?

The discount formula gives the amount taken off a listed price:

$$D = \text{MP} - \text{SP}$$

As a percentage of the original price it becomes

$$d = \frac{\text{MP} - \text{SP}}{\text{MP}} \times 100$$

The marked price is the denominator in every case. A discount describes a reduction from the listed price, so that listed price is the base.

Why the Base Is the Marked Price

A percentage is meaningless without the quantity it is a percentage of. Taking 20 per cent off a 500 item means 20 per cent of 500, giving 100, not 20 per cent of the 400 that remains.

If a discount were measured against the selling price, the same money reduction would report a different rate, which is why both retail convention and the formula fix the marked price as the denominator. That is also what makes the rearranged form work: $1 - \frac{d}{100}$ is the fraction of the marked price the customer still pays.

Variable Key

Examples of the Discount Formula

Example 1

An item marked 500 sells for 400. Find the discount and the discount percentage.

$$D = 500 - 400 = 100$$ $$d = \frac{100}{500} \times 100 = 20$$

Final answer: A discount of 100, which is 20 per cent.

Example 2

A shop offers 20 per cent off, then a further 10 per cent off at the till. Find the single equivalent discount.

The two reductions look as though they add to 30 per cent. Test it on a marked price of 1,000.

After 20 per cent the price is 800. The second 10 per cent is taken on 800, not on 1,000, so it removes 80 rather than 100, leaving 720.

A single 30 per cent discount would have left 700, so the two offers are not equivalent. Multiplying the retained fractions gives the correct result:

$$0.80 \times 0.90 = 0.72, \qquad d = (1 - 0.72) \times 100 = 28$$

Final answer: A single equivalent discount of 28 per cent.

Example 3

A jacket marked 2,400 carries a 35 per cent discount. Find the selling price.

$$\text{SP} = 2400\left(1 - \frac{35}{100}\right) = 2400 \times 0.65 = 1560$$

Final answer: 1,560

Example 4

A book sells for 255 after a 15 per cent discount. Find the marked price.

The selling price is 85 per cent of the marked price, so divide rather than multiply:

$$\text{MP} = \frac{255}{0.85} = 300$$

Final answer: 300

Working backwards means dividing by the retained fraction. Adding 15 per cent to 255 would give 293.25, which is not the marked price.

Example 5

An item costing 180 is marked up to 250 and then sold at a 12 per cent discount. Find the selling price and say whether the shop still profits.

$$\text{SP} = 250 \times 0.88 = 220$$

Final answer: The selling price is 220, which exceeds the 180 cost, so the shop makes 40. Discount is measured from the marked price and profit from the cost price, so the two percentages have different bases.

Don't Confuse Discount With These Three

Discount and percentage decrease are the same calculation under different names, with the marked price playing the role of the original value.

Where Do Students Trip Up on the Discount Formula?

Mistake 1: Adding successive discounts

Where it slips in: Two percentages in the same offer look additive, and adding is quicker than multiplying.

Don't do this: Treat 20 per cent then 10 per cent as 30 per cent.

The correct way: Multiply the retained fractions, $0.80 \times 0.90 = 0.72$, giving 28 per cent. The second discount applies to an already reduced price.

Students who convert each percentage into the fraction the customer still pays, before touching the numbers, get successive discounts right every time. The habit also settles the order question, since multiplication commutes and the order of two discounts never changes the final price.

Mistake 2: Taking the percentage on the selling price

Where it slips in: The selling price is the number in front of the customer, so it becomes the reference.

Don't do this: $\frac{100}{400} \times 100 = 25$ per cent for a 500 item sold at 400.

The correct way: $\frac{100}{500} \times 100 = 20$ per cent. The marked price is the base.

Mistake 3: Adding the percentage back to recover the marked price

Where it slips in: Reversing a 15 per cent discount feels like adding 15 per cent.

Don't do this: $255 + 15$ of $255 = 293.25$.

The correct way: Divide by the retained fraction, $\frac{255}{0.85} = 300$. Adding a percentage back always undershoots, because the two percentages are taken on different bases.

Key Takeaways

• The discount formula is $D = \text{MP} - \text{SP}$, with the percentage taken on the marked price.

• The rearranged form $\text{SP} = \text{MP}(1 - \frac{d}{100})$ treats the bracket as the fraction still paid.

• Successive discounts multiply rather than add, so 20 then 10 per cent is 28 per cent in total.

• Recovering a marked price means dividing by the retained fraction, never adding the percentage back.

• To work through commercial arithmetic with a teacher, explore a 7th grade math tutor or math classes online.

A Practical Next Step

Find the single equivalent discount for 25 per cent followed by 20 per cent. Then recover the marked price of an item sold at 714 after a 30 per cent reduction.

Want a live Bhanzu trainer to walk through more commercial arithmetic problems? Book a free demo class.

Read More

• Selling Price Formula

• Percent Decrease Formula

• Profit Formula

• Profit and Loss Formula

• What Is a Percent