Discount and marked price

Walk into any shop and you will see a price tag — say ₹2,500 on a pair of shoes — and then, at the counter, a smaller number on the bill. The tag price is called the Marked Price, and the gap between it and what you actually pay is the Discount. This chapter, the second half of ICSE Class 8's "Profit, Loss and Discount," teaches you to move confidently between Marked Price (MP), Discount, Discount percent, and Selling Price (SP) — in any direction the question demands. The one habit that decides most marks here is remembering what the discount percentage is calculated on: not the cost price, not the selling price, but always the marked price. Get that base right, and the rest is straightforward percentage arithmetic you already know from profit and loss.

The core insight

Discount is the reduction from Marked Price to Selling Price, and Discount percent is always computed on the Marked Price: $\text{Discount\%} = \dfrac{MP - SP}{MP} \times 100$ .

The core idea

A shopkeeper tags every article with a Marked Price (MP) — a price set somewhat above what the item is actually meant to sell for. This headroom is deliberate: it lets the shopkeeper advertise a discount, which draws customers in, while the final price still covers costs and leaves a profit. The Selling Price (SP) is what the customer actually pays after the reduction, and the Discount is simply the difference.

\text{Discount} = MP - SP

where: $MP$ is the Marked Price (the tag price before any reduction), and $SP$ is the Selling Price (the amount actually paid). The discount is usually expressed as a percentage, and this is where most marks are lost or won:

\text{Discount\%} = \frac{MP - SP}{MP} \times 100

where: the base of the percentage is $MP$ , never $SP$ and never the Cost Price ( $CP$ ). This is the single most important fact in the whole chapter — contrast it with Profit/Loss percent, which is always calculated on $CP$ . Two different questions, two different bases, and the two calculations are not interchangeable. Once you know MP and a discount percent, you can jump straight to SP without first finding the discount amount:

SP = MP \times \frac{100 - \text{Discount\%}}{100}

and the same relation, rearranged, recovers MP when SP and the discount percent are known instead:

MP = SP \times \frac{100}{100 - \text{Discount\%}}

These three equations are really one idea viewed from three angles: MP, SP and Discount% are linked, and any two of them fix the third. A quick sanity check that catches most arithmetic slips: for a genuine discount, $SP$ must always be less than or equal to $MP$ . If your working produces $SP > MP$ , or a negative discount, stop and recheck — you almost certainly used the wrong base or subtracted in the wrong order. Because every article also has a Cost Price, many exam questions weave this chapter together with Profit and Loss: you might be given $CP$ and $MP$ , and asked what discount percent still leaves a target profit percent. The trick is to keep the two chains separate on paper — MP→SP is the discount chain, CP→SP is the profit/loss chain — and only combine them at the very last step, through the shared value of $SP$ . It also helps to notice when the reverse formula is the one a question actually wants. If a shirt is sold for ₹1,020 after a known 15% discount, and the question asks for the Marked Price rather than giving it, plugging into $MP = SP \times \dfrac{100}{100 - \text{Discount\%}}$ directly gives $MP = 1020 \times \dfrac{100}{85} = ₹1200$ — far faster than guessing an MP and checking it by trial. Recognising which of the three quantities (MP, SP, Discount%) is missing, before reaching for a formula, is what separates a confident answer from a slow one.

Figure

A bar showing Marked Price split into Selling Price and Discount for the shoe example

Derivation AGetting Selling Price directly from Marked Price and Discount percent

The goal is to show algebraically why $SP = MP \times \dfrac{100 - \text{Discount\%}}{100}$ is exactly equivalent to computing the discount amount first and then subtracting it, so that a student can trust the shortcut formula instead of always doing two separate steps in every problem.

Step 1. Start from the definition of discount percent, with $d$ standing for the numerical value of the discount percentage: $d = \dfrac{MP - SP}{MP} \times 100$ .

Step 2. Divide both sides by 100 and multiply through by $MP$ to isolate the discount amount: $\dfrac{d}{100} \times MP = MP - SP$ .

Step 3. Rearrange to make $SP$ the subject: $SP = MP - \dfrac{d}{100} \times MP = MP\left(1 - \dfrac{d}{100}\right)$ .

Step 4. Write $1$ as $\dfrac{100}{100}$ and combine the fraction: $SP = MP \times \dfrac{100 - d}{100}$ , which is exactly the shortcut formula. It is not a separate rule to memorise — it is the same discount definition, just solved for $SP$ instead of for $d$ , and it saves a step whenever MP and discount percent are both given up front.

Worked example

A pair of shoes is marked at ₹2,500, and the shopkeeper offers a discount of 15%.

Step 1. Find the discount amount using MP as the base: $\text{Discount} = \dfrac{15}{100} \times 2500 = ₹375$ .

Step 2. Subtract to get the Selling Price: $SP = MP - \text{Discount} = 2500 - 375 = ₹2125$ .

Step 3. Check with the direct shortcut formula: $SP = 2500 \times \dfrac{100 - 15}{100} = 2500 \times \dfrac{85}{100} = ₹2125$ , matching Step 2. The customer pays ₹2,125, having saved a discount of ₹375.

Competitive stretch

Now push the same shoes through a mixed profit/loss-and-discount question: the shopkeeper's Cost Price for these shoes was ₹1,700. Did offering the 15% discount still leave a profit?

Step 1. The Selling Price from above is already known: $SP = ₹2125$ .

Step 2. Find profit using $CP$ as the base — a completely separate calculation from the discount one: $\text{Profit} = SP - CP = 2125 - 1700 = ₹425$ .

Step 3. Convert to profit percent: $\text{Profit\%} = \dfrac{425}{1700} \times 100 = 25\%$ . So even after giving a 15% discount off the marked price, the shopkeeper still made a 25% profit on cost — the discount reduced the tag price, but the tag was set high enough in the first place to absorb that cut and still turn a healthy profit.

Common traps

Calculating discount% on SP or CP instead of MP. Discount is always a percentage of the Marked Price — this is the single most common error in this chapter.
Confusing MP with SP. The Marked Price is the tag price before any reduction; the Selling Price is what is actually paid after the discount is applied. They are equal only when the discount is 0%.
Assuming discount% and profit% must relate directly. They don't — discount connects MP and SP, profit connects CP and SP, and a shopkeeper can offer a large discount while still making a healthy profit.
Adding the discount instead of subtracting. A genuine discount always makes SP less than or equal to MP; a negative discount in your working is a signal to recheck the arithmetic, not a valid answer.
Using the SP-based shortcut when SP is unknown, or vice versa. Before picking a formula, write down which of MP, SP and Discount% the question actually gives you — that decides whether you subtract first, or jump straight to the shortcut formula for SP or for MP.

Ask the tutor: Stuck on a mixed question that gives CP, MP and SP together and asks for both discount% and profit%? Ask the AI tutor to walk through it with you, one base price at a time.

Why do shops mark items higher than what they plan to sell them for

Marking up gives the shopkeeper room to advertise an attractive discount, which draws customers in, while the actual price paid still comfortably covers the cost price and leaves a profit. A "50% off" sale looks generous to a buyer, but the marked price was usually planned in advance so that even after the cut, the shopkeeper still comes out ahead. The tag price and the intended selling price are rarely meant to be the same number.

Is discount percent ever calculated on the Selling Price instead of the Marked Price

No, not in this chapter. By definition, $\text{Discount\%} = \dfrac{MP - SP}{MP} \times 100$ always uses Marked Price as the denominator. This mirrors how Profit and Loss percent always uses Cost Price as its denominator — each chapter has its own fixed base, and mixing them up is the most common source of wrong answers on this topic.

How is this different from Profit and Loss, since both involve Selling Price

Discount links Marked Price and Selling Price: it tells you how much was cut from the tag price. Profit and Loss links Cost Price and Selling Price: it tells you how the shopkeeper did financially. Selling Price is the one quantity both chains share, which is why combined problems give you CP, MP and SP together and expect you to apply the correct formula — MP-based or CP-based — to each part of the question separately.

Discount and marked price

The core idea

Worked example

Competitive stretch

Common traps

Before this

Where this leads