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A discount rate is defined as the percentage of the discount offered on any item. Discount can be calculated by finding the difference between the market price on the item and the selling price, or the price at which the item is sold. The reduction rate from the marked price and the sold price is the discount rate. In this article, we will discuss the discounts, related formulas, and their calculations in a short, crisp and lucid manner with some examples as well.
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Key Terms: Discount Rate, Marked Price, Selling Price, Commodity, Percentage
Discount Rate
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The reduced price of any commodity or service is known as the Discount rate. It can be counted as the difference between the marked price and the selling price of any commodity or service.
Marked price & selling price- It is the cost generally set up by the seller as per the market standards while the selling price is the price at which commodities or product has been sold. When the selling price is less than the marked price, then the buyer has said to be got some discount on it as you get when you shop during any festival.
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What is Discount Rate?
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It is the annualized percentage of the above discount, which is percentage adjusted, to give an annual percentage. The reduction in prices or rates on some items or products is referred to as Discount rate. It is generally printed on the price tags by making some modification in the marked price or by making changes in the retail price usually done by pasting a sticker on the commodity or making changes in the list price set for buyers.
What is Discount Provided?
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- For increasing the sales of the product.
- To encourage the distributor.
- To clear out the old stocks so that fresh arrival of items can be accommodated.
- To reward potential customers.
So, we can definitely say that discounts can act as a strategy to attract the customer/ consumers to particular goods and services. It is the easiest way to increase the demand for certain products. In Maths, the Discount problem can be solved using the Discount formulas. It helps the seller to increase the sales of the products and services.
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Discount Rate Formula
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Discount Rate = Marked price(M.P) – Selling price(S.P)
Here, M.P (Marked Price) is the actual price of the product that is without any discount.
& S.P (Selling Price) is what customers have to pay for the product.
OR Discount is the percentage of the market price, in the formula it can be depicted as:
Discount rate (DR)= p x r
Where p = principal amount
r = interest rate
Since we are with the Discount rate formula let’s quickly move to another topic i.e., How to find or calculate Discount Rate.
Calculation of Discount Rate
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Firstly, we should know the marked price and selling price of the product for the calculation of the discount rate. Simply, you have to use the formula given above to understand the concept.
For more clearance, let us look into some solved examples below so that you can solve any discount-related sums very easily.
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Discount Rate Examples
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Example 1. Radha purchased a top for Rs. 300. The discount offered for the top is 10%. Find how many rupees she has to give to the shopkeeper?
Ans. To solve the problem like this you need to be very clear about what is being given in the question and what we need to find.
Here, principal amount p= 300 rupees
Interest rate r = 10%
Discount rate, DR= p x r
DR = 300 x 10% = 300 x 10/100 = 30
So, the discount amount for the dress is 30
Now, dress rate = Principal amount – Discount rate
= 300 – 30 = 270 rupees.
Radha has given 270 rupees to the shopkeeper.
Things to remember
- The discount rate is the annualized percentage of the above discount, which is percentage adjusted, to give an annual percentage.
- The formula of discount rate: Discount Rate = Marked price(M.P) – Selling price(S.P)
- Another formula for Discount rate: Discount rate (DR)= p x r
- The market price is the price set up by the seller while
- Selling price is the price at which the product has been sold.
- Discount is generally given to the customers to increase the sales of the products.
Sample Questions
Ques.1. A shop selling mixer grinder offers 3% discount on all the cash purchases. What cash amount does Rita pay for washing machine the price of which is marked Rs. 850? (2 Marks)
Solution: Given, M.P = Rs 850
Discount rate=3%
So, 3% of M.P = 3/100 x 850
= Rs 25.5
S.P = M.P – Discount Rate(DR)
= 850 – 25.5
= Rs 824.5
So, Rita has to pay Rs 824.5 for the mixer grinder after getting discount of 3%.
Ques.2. The marked price of a table fan is Rs 720. During a season sale, it is sold out for Rs. 684. Find the discount offered on the table fan? (3 Marks)
Solution: Given, M.P = Rs 720
S.P = Rs 684
By using the discount formula,
Discount = M.P – S.P
= 720-684 = Rs 36
Now, here we have to find Discount rate offered. So,
Discount Rate = (Discount/ M.P) x 100
= 36/ 720 x 100
=5%
So, the offered discount% on the table fan is 5%
Ques.3. On the Diwali festival the shopkeeper allows his customers 10% off on the marked price of the goods but he still earns the profit of 25%. What is the actual cost to him of an article marked Rs. 250? (5 Marks)
Solution: Given, 10% off on the marked price, and M.P = 250 Rs.
Discount offered = 10%
Put the formula,
Discount = (M.P x Discount Rate) / 100
= (250 x 10) /100
= Rs 25
Now, S.P =M.P – Discount
= (250 -25) = Rs 225
And 25% profit he gets additionally,
Hence, buy using formula,
C.P(cost price) =100/ (100 +gain%) x S.P
= 100/(100 +25) x 225
= 100/125 x 225
= 180 Rs.
So, the actual cost of the article is Rs 180.
Ques.4. Ram purchased a watch of Rs 500 and the discount offered on the watch was 10%. Find the price of the watch after discount offered? (3 Marks)
Solution: Given, principle amount p =500 Rs
Interest rate r = 10%
Discount rate, DR= p x r
DR = 500x 10% = 500 x 10/100=50
So, the discounted amount of the watch is 50
Now, Selling price(S.P) of the watch = Principal amount – discount rate
= 500- 50 = 450
So, the price of watch after discount offered is Rs 450
Ques. 5. An umbrella marked at Rs 80 is sold for Rs 68. Find the discount rate? (3 Marks)
Solution. Given, M.P= 80 Rs
S.P= 68Rs
Discount rate = ?
By using the discount formula,
Discount = M.P – S.P
80 – 68 = Rs 12
Now, here we have to find Discount rate offered. So,
Discount Rate = [(Discount/ M.P) x 100]%
DR=[ (12/ 80) x 100] %
DR = 15%
So, the discount rate is 15%
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