Introduction:
There are four types of prices:
1. Cost Price: The amount paid by the vendor to purchase an product is called its cost price.
2. Selling Price: The amount at which the product is sold by the vendor is called its selling price.
3. Marked Price: The price that has been written on the pack or label of an product is called its marked price.
4. List Price: Electrical, electronics and other such goods don't contain labels or price marks. The retailer is supposed to sell them according to a list supplied by the manufacturer. The price which is given in the list is called the list price.
Definition of Discount:
Discount is defined as a certain percent of rebate is given on the marked price or the list price for payments. This rebate is known as Discount.
Formulas Related to the Discount Definitions:
1. Gain = Selling Price - Cost Price
2. Loss = Cost Price - Selling Price
3. Profit Percent (% ) = $\frac{profit * 100}{cost price}$
4. Loss Percent (%) = $\frac{loss * 100}{cost price}$
5. Selling Price = {$\frac{100+profit percent}{100}$} * cost price
6. Cost Price = {$\frac{100}{100+profit percent}$} * selling price
7. Cost Price = {$\frac{100}{100 - loss percent}$} * selling price
Selling price = Marked price - discount
8. Selling Price = $(\frac{100 - loss percent}{100})$ * cost price
Successive Discount:
Definition:
If two or more discounts are allowed one after the other, such discounts are known as successive discounts.
SUCCESSIVE DISCOUNTS:
Sometimes it is so happens that a company declares more than one discount on some articles. Such discounts are called successive discounts series.
Suppose a company marks the price of a table fan for $100 with discounts of 40% and 20%. To find the price at which the company ultimately sells the fan to their customer. We proceed as follows.
First method: Let the marked price be $100
Less 40% discount = $40
Price after first discount = $60
Less 20% discount = $12
Price after first discount = $48
$\rightarrow$the selling price becomes 48% of marked price.
Therefore, price at which company sells the fan after allowing two discounts is $48.
Second Method: It is convenient to find the single discount equal to the two discounts of 40% and 20%.
Formula = d1 + d2 - $\frac{d_1 * d_2 }{100}$
= 40 + 20 - $\frac{40 * 20 }{100}$
= 60 - 8
= 52
From above we see that the company chargers 48% i.e., it gives 52% discount on the marked price.
Single discounts equal to two successive discounts or discounts series of 40% + 20% is 52%.
Thus total discount of = 52% of 100 = $52
Therefore, Selling price of the company = $100 - $52 = $48.
Example Problems on Discounts:
1. The marked price of a camera is $300. 5% discount is allowed on each payment. Find the amount to pay for the camera.
Sol: Marked price = $300
5% discount on 300 = $\frac{5}{100}$ * 300
= $15
Selling price = Marked price - Discount
= 300 - 15 = $285
Therefore, the amount paid for the camera after discount is $285.
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2. A vendor offers a discount of 10% on a radio and still makes a profit of 26%. What is the actual cost to him if the marked price is $840?
Sol: Marked Price = $840
10% discount on $840 = $84.
Selling Price = Marked Price - discount
= 840 - 84 = $756
Profit = 26% if he sells it to %756.
So, Cost Price = $\frac{100}{100+26}$ * 756 = $600
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3. A car's marked price is $6000. The vendor allows successive discounts of 10% and 5% on it. What is the net selling price?
Sol: Marked price = $6000
Less 10 discount = $600
Price after first discount = $5400
Less 5% discount = $1350
Prince after 2nd discount = $4050
The net selling price after two successive discounts is $4050.
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4. If a discount of 20% off the marked price of a desk results in a savings of $20, what is the discounted price of the desk?
Sol: If marked price is m
0.2 m = $20
m = $100
Discounted price of the desk or cost price is $100 - $20 or $80.
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