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
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%) |
Additional Points:
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