__Discount__

The discount is referred to the reduction in the price of some commodity or service. It may anywhere appear in the distribution channel in the form of modifications in marked price (printed on the item) or in retail price (set by retailer usually by pasting a sticker on the item) or in list price (quoted for the buyer). The discount is provided for the purpose of increasing sales, to clear out old stock, to encourage distributors, to reward potential customer etc. In short, the discount can serve as a way to attract customers for a particular item or service.

In math, discount is one of the easiest way to raise the customers of particular product. Discounts are a significant element of your online merchandising plan. You build discounts so that you can force sales on items or collection of products to your customers who convene particular conditions. In math, the discount problems can be solved by using discount formula.

The “discount rate” means the interest rate. Discount rate is based on the simple interest rate. To calculate simple interest rate, just find out the interest rate for one period (multiply by amount, interest rate, period) but calculate the discount rate, just multiply by the amount and an interest rate. This is called the define discount rate.

To calculate the discount rate, just multiply the amount by an interest rate. By using the Formula **Discount rate DR = pr **(**p = principal amount**, **r = interest rate**).

**What is Discount Rate?**

Discount rate is one of the simple ways to increase the customers of particular product. Discounts are a important element of your online merchandising strategy. You make discounts so that you can force sales on products or collection of products to your customers who meet certain particular conditions.

The formula used to calculate the discount is discount = marked price – selling price.

Here,

Selling price is what you actually pay for the item.

Marked price is the normal price of the item without a discount.

Discount is either a dollar rate or a percentage of the marked cost.

**Discount Rate Definition**

Discount Rate is the cost of the total amount generally less than its original value is called . In other words, a total bill will generally sell at a discount, and the discount rate is annualized percentage of this discount, that is percentage is adjusted to give an annual percentage.

**Discount Rate Formula**

Formula of the Discount Rate is:

** **

**Discount rate DR = pr**

where,

- p = principal amount
- r = interest rate

** Questions**:

__Level-I__

**1: **Ricky purchase the dress. That dress rate was Rs1000 at 10% discount . Find discount rate? And then ricky how many dollars give to cashier?

**2: **Kalvin purchased land for 50000 dollars at 20% in 2000th year. Then 2004th year that land sales 3000 dollars. How many dollars he loss?

- The marked price of a ceiling fan is $ 1250 and the shopkeeper allows a discount of 6% on it. Find the selling price of the fan.
- A trader marks his goods at 40% above the cost price and allows a discount of 25%. What is his gain percent?
- A dealer purchased a washing machine for $ 7660. He allows a discount of 12% on its marked price and still gains 10%. Find the marked price of the machine.
- How much per cent above the cost price should a shopkeeper mark his goods so that after allowing a discount of 25% on the marked price, he gains 20%?
- Find the single discount equivalent to two successive discounts of 20% and 10%.
- A merchant who marked his goods up by 50% subsequently offered a discount of 20% on the marked price. What is the percentage profit that the merchant make after offering the discount?

- Applied to a bill for Rs. 1,00,000 the difference between a discount of 40% and two successive discounts of 36% and 4% is:
- On a 20% discount sale, an article costs Rs. 596. What was the original price of the article?

__Level-II:__

- A discount of 15% on one article is the same as discount of 20% on a second article. The costs of the
- A discount of 2 ½% is given to the customer on marked price of an article. A man bought the article for Rs. 39. The marked price of article is:
- Printed price of an article is Rs. 900 but the retailer gets a discount of 40%. He sells the article for Rs. 900. Retailer’s gain percent is:
- The marked price of a watch was Rs. 720. A man bought the same watch for Rs. 550.80, after getting two successive discounts. If the first discount was 10%, what was the second discount rate?
- A shopkeeper marks his goods 20% above cost price, but allows 30% discount for cash. His net loss is:
- A retailer buys 40 pens at the marked price of 36 pens from a wholesaler. If he sells these pens giving a discount of 1%, what is the profit percent?
- A pizzeria has a coupon that reads, “Getoff a $9.00 cheese pizza.” What is the discount? What is the sale price of the cheese pizza?

18.In a video store, a DVD that sells for $15 is marked, “10% off.” What is the sale price of the DVD?

__Answers:__

__Level-I:__

**Solution:1**

Here,

Principal amount p = 1000 rs

Interest rate r = 10%

Discount rate DR = pr

DR = 1000*

= 100

The discount amount for the dress is 100.

Discount rate DR = 100.

Dress rate = principal amount – discount rate

= 1000 – 100

=900

Ricky gives 900 rs to cashier

**Solution:2**

Principal amount p = 50000 dollars

Interest rate r = 20%

Discount rate DR = pr

DR = 50000 x 2010020100 in 2000th year

= 10000

Discount rate DR = 1000 dollars in 2000th year.

The discount amount is 10000 dollars.

Discount rate DR = 50000*30/100 in 2004th year

Discount rate =15000 dollars.

The discount amount is 15000 dollars.

Loss Discount rate in 2004th year – Discount rate in 2000th year

=15000 dollars – 10000 dollars

=5000 dollars

Kalvin 5000 dollars losses in that land.

**Solution:3**

Marked price = $ 1250 and discount = 6%.

**Discount = 6% of Marked Price**

= (6% of $ 1250)

= $ {1250 × (6/100)}

= $ 75

**Selling price = (Marked Price) – (discount) **

= $ (1250 – 75)

= $ 1175.

Hence, the selling price of the fan is $ 1175.

**Solution:4**

Let the cost price be $ 100.

Then, marked price = $ 140.

**Discount = 25% of Marked Price **

= (25% of $ 140)

= $ {140 × (25/100)

= $ 35.

**Selling price = (marked price) – (discount) **

= $ (140 – 35)

= $ 105.

Gain% = (105 – 100) % = 5%.

Hence, the trader gains 5%.

**Solution:5**

Cost price of the machine = $ 7660, Gain% = 10%.

Therefore, selling price = [{(100 + gain%)/100} × CP]

= $ [{(100 + 10)/100} × 7660]

= $ [(110/100) × 7660]

= $ 8426.

Let the marked price be $ x.

Then, the discount = 12% of $x

= $ {x × (12/100)}

= $ 3x/25

Therefore, SP = (Marked Price) – (discount)

= $ (x – 3x/25)

= $ 22x/25.

But, the SP = $ 8426.

Therefore, 22x/25 = 8426

⇒ x = (8426 × 25/22)

⇒ x = 9575.

Hence, the marked price of the washing machine is $ 9575

**Solution:6**

Let the cost price be $ 100.

Gain required = 20%.

Therefore, selling price = $ 120.

Let the marked price be $x.

Then, discount = 25% of $x

= $ (x × 25/100)

= $ x/4

Therefore, selling price = (Marked Price) – (discount)

= $ {x – (x/4)

= $ 3x/4

Therefore, 3x/4 = 120

⇔ x = {120 × (4/3)} = 160

Therefore, marked price = $ 160.

Hence, the marked price is 60% above cost price.

**Solution:7**

Let the marked price of an article be $ 100.

Then, first discount on it = $ 20.

Price after first discount = $ (100 – 20) = $ 80.

Second discount on it = 10% of $ 80

= $ {80 × (10/100)} = $ 8.

Price after second discount = $ (80 – 8) = $ 72.

Net selling price = $ 72.

Single discount equivalent to given successive discounts = (100 – 72)% = 28%

**Solution:8** The easiest way to solve these kinds of problems is to assume a value for the merchant’s cost price.

To make calculations easy, it is best to assume the cost price to be $100.

The merchant marks his goods up by 50%.

Therefore, his marked price (quoted price) = cost price + mark up.

Marked price = $100 + 50% of $100 = 100 + 50 = $150.

The merchant offers a discount of 20% on his marked price.

Discount offered = 20% of 150 = $30.

Therefore, he finally sold his goods for $150 – $30 = $ 120.

We assumed his cost to be $100 and he sold it finally for $120.

Therefore, his profit = $20 on his cost of $ 100.

Hence, his % profit = profit/cost price * 100 = 20/100*100 = 20%.

**Solution:9 **40% of Rs. 1,00,000 = Rs. 40,000

36% of 1,00,000 = 36000

4% of 36,000 = Rs. 2,560.

Therefore, two successive discounts on Rs. 1,00,000 = 36,000 + 2560 = Rs. 38,560.

Difference between a discount of 40% and two successive discounts of 36% and 4%

= 40,000 – 38,560

= Rs. 1,440

**Solution:10 **If the selling price of the article is S, then

S – 20% of S = 596

S – S/5 = 596

4S/5 = 596

⇒ S = 596 x 5/4

⇒ S = 745

__Level-II__

**Solution:11**Let the prices of two articles be X and Y

From the question 15X/100 = 20Y/100

X/Y = 20/15

Thus the ratio of prices of two articles is 4 : 3

Any two amounts in the ratio 4 : 3 will satisfy the condition.

In the above instance, Rs. 80 and Rs. 60 is the answer.

**Solution:12 **Formula for Marked Price = 100 x SP/(100 – d%) = 100 x 39/(100 – 2.5%)

= 3900 / 97.5

= Rs. 40.

Marked Price of Article is Rs. 40.

**Solution:13 **Retailer gets a discount of 40% means he buys it at 60% of the price

60% x 900 = Rs. 540

Profit on selling it at Rs. 900 = 900 – 540 = Rs. 360.

Profit % = (Profit / C.P) x 100 = (360 / 540) x 100 = 66^{2}/_{3}

Retailer’s Gain percent is 66^{2}/_{3}

**Solution:14**10% discount on 720 = Rs. 72

Cost after 1st discount = 720 – 72 = Rs. 648.

Cost after 2nd discount = Rs. 550.80

Therefore 2nd discount = 648 – 550.80 = Rs. 97.20

Discount % = (97.2 x 100)/648 = 15%

Second discount rate = 15%.

**Solution:15 **Let the cost price be Rs. 100.

M.P. (which is 20% above C.P.) = Rs. 120.

30% discount on Rs. 120 = Rs. 36.

Selling Price = Rs. 120 – 36 = Rs. 84

Cost Price = Rs 100 and Selling Price = Rs 84 {since CP > SP, it is a loss}

Loss% = (16/100) x 100 = 16%.

His net loss percent is 16%.

**Solution:16 **Assuming the M.P. of each pen to be Rs. 10, the M.P. of 36 pens = Rs. 360

Cost price of 40 pens = Rs. 360 (from the question)

Cost price of each pen = 360/40 = Rs. 9

Selling Price of each pen at a discount of 1% on a marked price of Rs. 10 = 99% x 10 = Rs. 9.90

Profit = 9.90 – 9.00 = Rs. 0.90

Profit % = (0.90/9.00) x 100 = 10%

Profit % = 10%.

**Solution:17 **The discount is $3.00 and the sale price is $6.00

**Solution:18 **The rate is 10%. Thus, the customer is paying 90% for the DVD

The sale price is: 0.90 x $15.00 = $13.50

The sale price is $13.50.

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