4.2 Discounts:

Suppose you have a marriage function in your family and assume that as per tradition, your family   gifts Saris and ready made shirts to close family members.  There are 24 ladies who are to be given Saris and 16 men who are to be given Shirts. Assume also that identical materials are available in 2 different shops at the same rates (sale price of a Sari is Rs 350 and sale price of a ready made shirt is Rs 300). However, the two shop keepers offer different discount schemes as given below

Shop A:  The shop keeper offers a discount of 10% on total value purchased.

Shop B: for every 5 Saris one Sari is given free. For every 7 shirts one shirt is given free

Since you are the one who is in good mathematics, you have to advice your family in which shop they need to buy clothes, what is your advice?

Introduction:

During festivals and New Year very often we say advertisement on TV and news papers about discount sale.

Discount sale is about selling a product at lower price than what is marked on the product

You may ask question will not the merchant make loss by selling at a discount?

Some times he may incur loss. But most of the times he does not make loss but makes less profit.

Some of the circumstances under which discounts are made by manufacturer/Seller:

1. To increase sales during the period of offer

2. To clear the items which are in stock (could be old)

3. To get new customers

4. To promote a new product.

The discount offers could be as follows:

 Example Type of Discount 5% off on  geometry box Percentage discount Rs 10 off on football Cash discount Get  a voltage stabilizer with every TV Another product  free Buy three  shirts and  get one shirt  free Same product free

Thus

‘Discount’ = Marked price – Selling price = MP-SP or

‘Discount’ = Discount% *Marked price/100

and  ‘Selling  price’(SP)  = Marked price(MP)- discount

We can calculate Discount% as

Discount%= Discount*100/Marked price.

Discount % is also called rate of discount.

Marked price is also called some times as ‘List Price’.

4.2 Problem 1: With every purchase of TV which has a marked price of Rs 15,000,  a shopkeeper  gives  a Voltage stabilizer worth  Rs 1200 free. Find the effective rate of discount and selling price of TV.

Solution :

The discount offered here is in terms of a free product which is worth Rs1200 Discount =1200.

Selling Price (NP) = Marked price (MP) - discount = 15000-1200 =13,800

Discount% = Discount/Marked price = 1200*100/15000 = 8%

Verification :

Discount = Discount% *Marked price/100 = 8*15000/100 = 8*150 = 1200. This is the cost of Voltage stabilizer as given in the  problem.

4.2 Problem 2:  A bookseller gives 15% discount on books. If you purchased books totaling Rs 1500. How much discount have you get?

Solution:

Discount = Discount% *Marked price/100= 15*1500/100 = Rs225

Selling price (SP) = Marked price (MP)- discount = 1500-225 = Rs.1275

Verification : Discount%= Discount*100/Marked price= 225*100/1500  =15 which is the % discount given by shopkeeper.

as given in the problem

Given the rate of discount and selling price we can arrive at marked price by using the formula

MP = 100*SP/(100-discount%)

4.2 Problem 3 :   A company sells a sewing machine  at Rs 3520 by giving a discount of 12%. Find the marked price

Solution:

MP = 100*SP/(100-discount%) =100*3520/(100-12) = 100*3520/88 =  4000

Verification :  MP=4000.Discount % = 12. Discount = Discount% *Marked price/100 = 12*4000/100 = 480 Selling  price(SP)  = Marked price(MP)- discount = 4000-480 = 3520 which is as given in the problem

4.2 Problem 4 :  A customer saved Rs 20 by buying 10 soaps.10% discount was allowed on each soap. Find the marked price of each soap.

Solution:

We are given  the savings(discount) and discount% and are asked to find MP.

Since the customer saved Rs 20 on 10 soaps, his saving is Rs 2 on one soap

We know

Discount = Discount% *Marked price/100 2 = 10*MP/100 ( discount = 2 and discount% =10) 200 = 10*MP (Multiply both sides by 100) 20=MP

Verification :

MP = 20, discount is 10% Discount = Discount% *Marked price/100 = 10*20/100 = Rs 2 Savings on buying 20 soaps = Number of soaps*saving per soap = 10*2 = Rs20 which is as given in the problem

4.2 Problem 5 : Suppose you have a marriage function in your family and assume that as per tradition, your family   gifts Saris and ready made shirts to close family members.  There are 24 ladies who are to be given Saris and 16 men who are to be given Shirts. Assume also that identical materials are available in 2 different shops at the same rates (sale price of a Sari is Rs 350 and sale price of a ready made shirt is Rs 300). However, the two shop keepers offer different discount schemes as given below

Shop A:  The shop keeper offers a discount of 10% on total value purchased.

Shop B: for every 5 Saris one Sari is given free. For every 7 shirts one shirt is given free

Since you are the one who is in good mathematics, you have to advice your family in which shop they need to buy clothes.

Solution:

Shop A

Sale price of 24 Saris = 24*350 =  Rs   8,400

Sale price of 16 shirts = 16*300 =  Rs   4,800

Total cost of clothes                   = Rs  13, 200

Discount = Discount% *Marked price/100 = 10*13200/100 = 1320

Selling price(SP)  = Marked price(MP)- discount = 13200-1320 = Rs 11,880

Shop B:

Since   we need 24 saris and the   shop keeper gives 1 sari free for every 5 Saris. We need to buy only 20 Saris

( 20 saris + 4 free saris = 24 saris)

Since   we need 16 shirts and the   shop keeper 1gives 1 shirt free for every 7 shirts. We need to buy only 14 shirts

( 14 shirts + 2 free shirts = 16 shirts)

Cost of 20 Saris = 20*350 = Rs   7,000

Cost of 14 shirts = 14*300 = Rs   4,200

Total selling price                = Rs  11,200

Since B’s selling price is less than A, Would you not suggest your family to buy from shop B even, if you are not given the saving amount of Rs 680 (11880-11200) ?

4.2 Summary of learning

 No Points to remember 1 Discount = Marked price – Selling price = MP-SP 2 Discount = Discount% *Marked price/100 3 Selling  price(SP)  = Marked price(MP)- discount 4 Discount%= Discount*100/Marked price. 5 MP = 100*SP/(100-discount%)

Successive discounts:  Some times discount on discount is given to promote sales. In such cases first discount is calculated on MP. The discount is subtracted from MP. The second discount is calculated on the resulting amount and is again subtracted. The amount left after subtracting the last discount is SP of the article.

4.2 Problem 6: Find which of the following successive discounts are beneficial to the buyer and find the equivalent single discount

(1) 30%, 20% and 10%

(2) 25%, 20% and 15%

Using the second successive discount, find the selling price of the product whose MP is Rs 300.

Solution:

Case 1:

Let the MP be Rs 100

Since the 1st discount is 30%

The 1st discount = 30% of 100 = 30 (The price of the product is reduced to Rs 70)

Since the 2nd discount is 20%

The 2nd discount = 20% of 70 = 70*20/100 = 14 (The price of the product is reduced by Rs 14 to Rs 56)

Since the 3rd discount is 10%

The 3rd discount = 10% of 56 = 56*10/100 = 5.6 Total discount = 30+14+5.6 = 49.6

Since Rs 100 product is sold at Rs 50.4 the effective discount is 49.6%.

Case 2:

Let the MP be Rs 100

Since the 1st discount is 25%

The 1st discount = 25% of 100 = 25 (The price of the product is reduced to Rs 75)

Since the 2nd discount is 20%

The 2nd discount = 20% of 75 = 75*20/100 = 15 (The price of the product is reduced by Rs 15 to Rs 60)

Since the 3rd discount is 15%

The 3rd discount = 15% of 60 = 60*15/100 = 9 Total discount = 25+15+9 = 49

Since Rs 100 product is sold at Rs 51, the effective discount is 49%.

It is clear from above that the first successive discount is beneficial to the buyer.

Since MP is Rs 300

Discount = 300*49/100 = 147 SP = MP - discount = 300 -147 = Rs 153