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Have you ever bought a new toy for 100 rupees and later sold it to a friend for 80 rupees? You just experienced 'loss'! Or maybe you saw a cool shirt priced at 500 rupees, but the shop offered it for 400 rupees. That's a 'discount'! In this chapter, we'll learn about how to calculate these everyday money situations, which are super important for your exams.
When a shop gives two discounts one after another (like '10% off, then another 20% off'), it's not simply 10% + 20% = 30% off. It's less! Use this trick to find the single big discount. It's like finding a single jump for two small steps.
Often in exams, you need to know how much a shopkeeper marks up (increases the price on the tag) their goods so that even after giving a discount, they still make a profit. This trick connects Cost Price (CP) and Marked Price (MP) directly. Think of it as a bridge between how much they bought it for and how much they wrote on the tag.
If you know how much money you got (Selling Price) and the loss percentage, you can quickly find the original Cost Price. Just think backwards! If you lost 20%, it means the selling price is 80% of the original cost. Use this idea to get back to the start.
When a shop gives a discount on a marked item, you want to quickly know the final price. Instead of finding the discount amount first and then subtracting, just find the percentage of the marked price you actually pay. If the discount is 15%, you pay (100-15)% = 85% of the marked price. Super fast!
Sometimes, problems give you relations like 'CP is 80% of SP' or 'Discount is 20% of MP'. Convert these percentages into simple fractions (like 80% = 4/5). This makes comparing Cost Price, Selling Price, and Marked Price super easy and avoids big calculations. Ratios simplify everything!
Imagine your mom buys a big pack of pencils for ₹50. This is the Cost Price (CP) – the money spent to get something. Later, you sell one pencil to your friend for ₹10. This is the Selling Price (SP) – the money you get for selling something.
When you sell the pencil for ₹10, and its part of the pack cost your mom less (let's say ₹5 per pencil), then your mom made a profit. But if you bought it for ₹10 and had to sell it for ₹8 because your friend only had ₹8, then you faced a Loss.
Now, let's talk about discounts. Have you ever seen a 'Sale' sign at a shop? It means they are giving things at a lower price than what's written on the tag. The price written on the tag is called the Marked Price (MP) or List Price. The amount reduced from this price is the Discount.
It's like a chain: you buy something (CP), you put a tag on it (MP, if you're selling it), you offer a discount on that tag (Discount), and then you finally sell it (SP). Sometimes, your SP might be less than your CP (Loss) even after marking it up and giving a discount, or it might be more (Profit).
Understanding these basic ideas helps you solve many complex problems quickly. Just think of them as simple money stories!
Loss
Loss = Cost Price (CP) - Selling Price (SP)Loss Percentage
Loss % = (Loss / CP) × 100Discount
Discount = Marked Price (MP) - Selling Price (SP)Discount Percentage
Discount % = (Discount / MP) × 100Selling Price with Discount
SP = MP × (100 - Discount %) / 100Relation between CP, MP, Discount & Profit/Loss
CP / MP = (100 - Discount %) / (100 + Profit % or - Loss %)| Concept | Definition | Calculated On |
|---|---|---|
| Loss | Selling for less than buying price | Cost Price (CP) |
| Discount | Reduction on the tag price | Marked Price (MP) |
| Cost Price (CP) | The original buying price | Self (Base for Loss/Profit) |
| Selling Price (SP) | The price at which something is sold | Can be CP or MP related |
| Marked Price (MP) | The price written on the tag | Self (Base for Discount) |
Q: A shopkeeper bought a chair for ₹700 and sold it for ₹630. What is the loss percentage?
Q: The marked price of a jacket is ₹1500. The shop offers a discount of 20%. What is the selling price of the jacket?
Q: By selling a bicycle for ₹2400, a person loses 25%. For what price should he sell it to gain 20%?
Q: A shop offers two successive discounts of 10% and 20% on an item marked at ₹1000. Find the single equivalent discount percentage.
You bought a new phone for ₹15,000. After two years, you sell it online for ₹9,000. How much money did you lose?
A new video game costs ₹2,000. During a holiday sale, it's advertised with a '25% off' sticker. What's the new price?
Your favorite T-shirt has a price tag of ₹800. The shop gives a 10% discount first, and then another 5% discount on the reduced price. What's the final price you pay?
A fruit seller bought 100 apples for ₹1000. Unfortunately, 20 apples spoiled, so he had to throw them away. He sold the remaining 80 apples for ₹12 each. Did he make a loss or a profit? How much?
If the selling price of 15 articles is equal to the cost price of 12 articles, find the loss percentage.
A dishonest shopkeeper sells goods at cost price but uses a weight of 900 grams instead of 1 kg. What is his profit percentage?
An item is sold at a 20% discount on its marked price. If the item costs ₹1200 to the seller, and he still makes a 10% profit, what is the marked price?
A dealer allows a 15% discount on the marked price. How much above the cost price must he mark his goods to make a profit of 19%?
1A book was bought for ₹200 and sold for ₹180. What is the loss amount?
2If an item's Marked Price is ₹500 and it is sold for ₹450, what is the discount amount?
3A fruit vendor bought oranges for ₹10 per dozen and sold them for ₹1 each. What is his loss percentage?
4A fruit vendor bought oranges for ₹10 per dozen and sold them for ₹0.75 each. What is his loss percentage?
5The marked price of a shirt is ₹800. After a 15% discount, what is the selling price?
6By selling a watch for ₹420, a person loses 20%. What was the cost price of the watch?
7An item is marked 30% above its cost price. If a discount of 10% is given, what is the profit percentage?
8A shop offers two successive discounts of 10% and 10%. What is the single equivalent discount?
9If the cost price of 20 articles is equal to the selling price of 25 articles, find the loss percentage.
10A shopkeeper gives a discount of 10% on an article and still gains 20%. If he gives a 20% discount, what is the new profit percentage?
11A dishonest shopkeeper sells rice at cost price but uses a false weight of 950 grams for 1 kg. What is his profit percentage?
When a shop gives two discounts one after another (like '10% off, then another 20% off'), it's not simply 10% + 20% = 30% off. It's less! Use this trick to find the single big discount. It's like finding a single jump for two small steps.
Often in exams, you need to know how much a shopkeeper marks up (increases the price on the tag) their goods so that even after giving a discount, they still make a profit. This trick connects Cost Price (CP) and Marked Price (MP) directly. Think of it as a bridge between how much they bought it for and how much they wrote on the tag.
If you know how much money you got (Selling Price) and the loss percentage, you can quickly find the original Cost Price. Just think backwards! If you lost 20%, it means the selling price is 80% of the original cost. Use this idea to get back to the start.
When a shop gives a discount on a marked item, you want to quickly know the final price. Instead of finding the discount amount first and then subtracting, just find the percentage of the marked price you actually pay. If the discount is 15%, you pay (100-15)% = 85% of the marked price. Super fast!
Sometimes, problems give you relations like 'CP is 80% of SP' or 'Discount is 20% of MP'. Convert these percentages into simple fractions (like 80% = 4/5). This makes comparing Cost Price, Selling Price, and Marked Price super easy and avoids big calculations. Ratios simplify everything!
Loss = Cost Price (CP) - Selling Price (SP)Loss % = (Loss / CP) × 100Discount = Marked Price (MP) - Selling Price (SP)+3 more formulas below