Profit, Loss and Discount: ICSE Class 7 Complete Guide

Every time you walk through a mall and see a sign saying 'flat 40% off plus an additional 10%', you are staring at an ICSE Class 7 Selina question in disguise. Is the total discount 50%? No, it is not. Parents who never studied commercial maths properly often overpay at sales, assume two percents simply add up and miss the real number by a few hundred rupees. This chapter is your chance to never be that person.

The three characters of this story are simple. The cost price is what you paid to buy something. The selling price is what you got when you sold it, or what you paid when you bought it at the shop. The marked price is the sticker price before any discount. Every formula in the chapter is just a way of comparing these three with each other.

Selina packs a lot of application problems into this chapter because it wants Class 7 students to leave with real numerical literacy. This guide walks through every formula, every worked example and every exam trap so your child can finish the chapter feeling confident.

Let us define the four terms you will use all chapter.

* Cost Price (CP): the price at which a shopkeeper buys an article from the wholesaler or manufacturer.
* Selling Price (SP): the price at which the shopkeeper sells the article to you.
* Marked Price (MP) or List Price: the price printed on the tag or advertised in the catalogue, before any discount.
* Discount: the reduction given on the marked price. The selling price after discount is $SP = MP - \text{discount}$.

The two derived quantities that form the heart of the chapter are:

* Profit: when $SP > CP$, the shopkeeper makes a profit. $\text{Profit} = SP - CP$.
* Loss: when $SP < CP$, the shopkeeper makes a loss. $\text{Loss} = CP - SP$.

If $SP = CP$, neither profit nor loss.

Remember: profit and loss are always computed with respect to the cost price. Discount is always computed with respect to the marked price. Mixing these up is the number one reason students lose marks.

Problem: Ravi bought a cycle for Rs 2500 and sold it for Rs 2800. Find his profit and profit percent.

Solution:

Step 1: Check if it is profit or loss. SP (2800) > CP (2500), so profit.

Step 2: Compute profit.

Step 3: Compute profit percent.

Ravi made a profit of Rs 300, or $12\%$.

Problem: Sita sold her laptop for Rs 18000 at a loss of $10\%$. Find the cost price.

Solution:

Step 1: Loss case, so use the loss formula for CP.

The cost price was Rs 20000.

Check: If CP is 20000, loss of $10\%$ means loss of Rs 2000, so SP is $20000 - 2000 = 18000$. Matches.

Many Selina questions ask you to find CP given SP and profit or loss percent. The trap is that students try to compute '$10\%$ of 18000' and add or subtract. Never do that. The percent is on the CP, not the SP. Use the correct formula.

The marked price is the tag price. The discount is a reduction from the marked price to arrive at the selling price.

And to find SP from MP:

Note that discount is always expressed as a percent of the marked price, never the selling price or cost price.

Worked example 3: A shirt is marked at Rs 800. The shopkeeper gives a discount of $20\%$. Find the selling price.

Solution:

The selling price is Rs 640.

Worked example 4: A book is marked at Rs 250. After a discount it sold for Rs 200. Find the discount percent.

Solution:
Discount $= 250 - 200 = 50$.

A $20\%$ discount was given.

This is the famous trap. When a shopkeeper gives two discounts one after the other, the total discount is not the sum of the two.

Worked example 5: A TV is marked at Rs 30000. The shopkeeper gives a $20\%$ discount, and then a further $10\%$ discount on the discounted price. Find the final selling price and the total effective discount percent.

Solution:

Step 1: Apply the first discount.
First discount $= 20\%$ of $30000 = 6000$.
Price after first discount $= 30000 - 6000 = 24000$.

Step 2: Apply the second discount on the new price.
Second discount $= 10\%$ of $24000 = 2400$.
Final SP $= 24000 - 2400 = 21600$.

Step 3: Find the effective discount.
Total discount (in rupees) $= 30000 - 21600 = 8400$.

Notice: the effective discount is $28\%$, not $20 + 10 = 30\%$. Successive discounts always produce less than the sum of the individual percents. This is because the second discount is calculated on a smaller base.

A quick shortcut for two successive discounts of $a\%$ and $b\%$:

For $a = 20$ and $b = 10$: $20 + 10 - \frac{200}{100} = 28\%$. Matches exactly.

This shortcut saves time in MCQs. ICSE usually expects you to show the step by step calculation in long answer questions, so use both methods.

The hardest Selina questions combine profit, loss and discount in one problem. Here is a typical example.

Worked example 6: A shopkeeper marks his goods $40\%$ above the cost price and offers a discount of $20\%$. Find his profit or loss percent.

Solution:

Step 1: Let CP be 100 (a convenient choice for percent problems).

Step 2: MP is $40\%$ above CP. $MP = 100 + 40 = 140$.

Step 3: Discount of $20\%$ on MP. Discount $= 20\%$ of $140 = 28$.

Step 4: $SP = MP - \text{discount} = 140 - 28 = 112$.

Step 5: Compare SP with CP. SP (112) > CP (100), so profit.
Profit $= 12$.
Profit percent $= \frac{12}{100} \times 100 = 12\%$.

The shopkeeper makes a $12\%$ profit despite offering a $20\%$ discount. This is exactly how real shopkeepers use markups to absorb discounts and still make money.

Notice the trick of letting CP $= 100$. When all quantities in the problem are in percents, this substitution turns tedious arithmetic into easy mental maths. Use it whenever you can.

Six errors that cost marks in ICSE Class 7 profit loss tests.

1. Wrong denominator in profit percent. Using SP instead of CP. Profit percent is always on the cost price.

2. Adding successive discounts. Writing 'a $20\%$ discount then a $10\%$ discount equals $30\%$ off'. It is actually $28\%$. Always apply discounts step by step.

3. Mixing up MP and CP. Writing the markup formula as 'discount on CP' instead of 'discount on MP'. Discount is always on marked price.

4. Forgetting the subtraction. After finding the discount amount, some students stop and call it the final answer. The final price is MP minus discount.

5. Dropping percent signs. Writing '12' in the final answer when the question asked for a profit percent.

6. Loss formula confusion. Using $\text{Loss}\% = \frac{\text{Loss}}{SP}$ by mistake. Loss is a percent of CP, not SP.

* Profit is $SP - CP$. Loss is $CP - SP$. Both are compared to CP.
* Profit percent and loss percent use CP as the denominator.
* Discount is $MP - SP$ and is compared to MP.
* Use $SP = CP(1 + \text{profit}\%/100)$ for profit cases, $SP = CP(1 - \text{loss}\%/100)$ for loss cases.
* Successive discounts do not add. Apply them one at a time or use the shortcut $a + b - ab/100$.
* In combined problems, let CP be 100 to simplify arithmetic when all values are in percents.
* Always verify your final answer by substituting back into the original problem.