PROFIT AND LOSS
Profit and loss deals with profit and loss made
in finance and business transaction.
If the selling price of the article is greater than
its cost price, it is called profit.
i.e S.P > C.P
Profit = S.P – C.P
If the selling price of the article is less than its
cost price, it is called loss.
i.e S.P < C.P
Loss = C.P – S.P
Discount:
The price of the article tagged by the
shopkeeper is the marked price of the article
Discount is the amount given on marked price
by lowering the price so that the shopkeeper
can promote his business and attract the more
customer. It is expressed in percentage. It is the
difference between marked price and selling
price.
S.P = M.P – discount
VAT (Value added tax)
Value-Added Tax (VAT) is a tax on consumer
spending. It is collected by VAT-registered
traders on their supplies of goods and services
affected within the State. Generally, each such
trader in the chain of supply from manufacturer
through to retailer charges VAT on his or her
sales and is entitled to deduct from this amount
the VAT paid on his or her purchases.
The effect of offsetting VAT on purchases
against VAT on sales is to impose the tax on the
added value at each stage of production –
hence Value-Added Tax.
VAT is imposed after the deduction of
discounts.
1. Davis bought a car listed at $ 536500 at 8% discount and then 10% sales tax charged on the discounted price. Find the amount Davis paid for the car.
Solution:
Given,
MP of car = $ 536500,
rate of discount,d% = 8%
Therefore, the amount of discount = $ (536500 X 8/100)
= $ 42920
Therefore, the selling price of the car =
$ (536500 - 42920)
= $ 493580.
The rate of sales tax = 10%
∴ the sale tax on the car = 10% of SP
= ¹⁰/₁₀₀×$493580
=$49368
Therefore, the amount paid by Davis
= $ (493580 + 49358)
= $ 542938.
2. Ron buys a car for $ 38,400 which includes 10% discount and then 6% sales tax on the marked price. Find the marked price of the car.
Solution:
Let the marked price of the car be P. Then, the discount on marked price = 10% of MP
= ¹⁰/₁₀₀MP = MP/10,
and sales tax = 6% of MP
= 6/100 P
= 3P/50
Therefore, the price paid = P – P/10 + 3P/50
= 24P/25
According to the problem we have,
24P/25 = $38400
P = $38400 × 25/24
= $1600 × 25
= $40000
Therefore, the marked price of the car is $40000.
3. Due to short supply in the market, a shopkeeper raises the price of a cycle by 5% above the marked price and charges a sales tax of 12 % on the marked price. A customer has to pay $ 4680 for the cycle. Find the marked price of the cycle.
Solution:
Let the marked price of a cycle be MP.
Then, the raised price = MP + 5% of MP
= MP + 5MP/100 = ²¹/₂₀MP
Sales tax = 12% of MP
= ¹²/₁₀₀MP = ³/₂₅MP
∴ the price payable = ²¹/₂₀MP + ³/₂₅MP
= ¹¹⁷/₁₀₀MP
According to the problem we get,
¹¹⁷/₁₀₀MP = $4680
MP = $4680 × 100/117
= $4000
∴ the marked price of the cycle is $4000.
4. Jack buys a laptop for $ 34821 which includes 10% rebate on the listed price and then 6% sales tax on the remaining price. Find the listed price of the computer.
Solution:
Let the listed price of the laptop be x,
Given,
rebate on the listed price = 10%
so, the amount of rebate = x * ¹⁰/₁₀₀
= $ x/10
Therefore, cost of the laptop after rebate
= $ x - $ x/10
= $ 9x/10
Since sale tax is 6% on the remaining price,
Therefore, the amount of sales tax
= $ 9/10x X 6/100
= $ 27/500 x.
Therefore, the net amount to be paid = $ 910x + $ 27/500 x
= $(9/10x + 27/500x)
According to the problem, we get,
9/10x +27/500x = 34821
Or, 477/500x = 34821
Or, x = 36500.
Therefore, the marked price of the laptop = $ 36500.
The calculation of sales tax is very easy as it involves very simple concept of percentage.
The government of every country needs money the following:
(i) to meet their administrative expenses,
(ii) to execute social welfare and development schemes,
(ii) to meet the expenses on salaries of its employees, etc.
One of the many sources of collecting money (revenue) by the government from the citizen on the sale of goods within their respective territories. This purpose is known as sales tax.
It is levied by a government on the sale of different commodity. The sales tax is the sum of money a buyer pays over and above the price of a commodity to buy it.
The rates of tax on purchase of different commodities within a country are different. Also, the rates of tax on the same commodity in different country are different. Some commodities may be be exempted from sales tax by a government. Sales tax is one of the many forms of indirect taxes that a government imposes on its citizens.
If M.P. be the printed price or marked price of a commodity, the rate of sales tax be VAT% and S.P. be the selling price (i.e., the price a customer has to pay), then
S.P. = M.P.+VAT% of M.P. and
sales tax = SP - MP
Solved examples on relation between printed
price, rate of sales tax and selling price:
1. The printed price of a bi-cycle is $ 4200. The rate of sales tax on it is 10%. Find the price at which the cycle can be purchased.
Solution:
Here, the printed price MP = $ 4200, the rate of sales tax = 10%,
i.e. VAT = 10%.
Therefore, the selling price
SP=M.P.+VAT% of M.P
= $ 4200 + 10% of $ 4200
= $ 4200 × $420
= $ 4620
Therefore, the cycle can be purchased for
$ 4620.
3. Mason purchased a pair of shoes costing $ 850. Calculate the total amount to be paid by him, if the rate of Sales Tax is 6%.
Solution:
The sale price of shoes = $ 850
and, the sales tax = 6 % of $ 850 = $ 51
Therefore, the total amount to be paid by Rohit = $ 850 + $ 51
= $ 901
4. John bought a printing machine for $5136, which includes sales tax. If the listed price of the printing machine is $ 4800, what was the rate of sales tax?
Solution:
Given,
the printed price (or listed price) MP = $ 4800, the selling price SP = $ 5136.
If the rate of sales tax be vat% then,
SP
⟹ $ 5136 = $ 4800 +vat% of $ 4800
⟹ vat = 7
Therefore, the rate of sales tax was 7%.
5. Jacob purchased an article for $ 702 including Sales Tax. If the rate of Sales Tax is 8%, find the sale price of the article.
Solution:
Let the sale price of the article be $ x
Therefore, x + 8% of x = $ 702
⟹ x + ⁸/₁₀₀x= $ 702
⟹ 108x/100= $ 702
⟹ x = $ 702 ×¹⁰⁰/₁₀₈
⟹ x = $ 650
Therefore, sale price of the article = $ 650
6. Find the marked price of a motorbike which is bought at $ 36300 after paying a sales tax at the rate of 10%.
Solution:
Let, the marked price or listed price be MP,
Given, the selling price SP = $ 36300
and the rate of sales tax V% = 10%,
Now, SP= MP + V% of MP
⟹ $ 36300 = MP + ¹⁰/₁₀₀*MP
⟹ MP* ¹¹⁰/₁₀₀= $ 36300
⟹ P = $ 36300 ×¹⁰⁰/₁₁₀
⟹ P = $ 33000
Therefore, the marked price is $ 33000.
4. A refrigerator is marked for sale at $ 17600 inclusive of sales tax at the rate of 10%. Calculate the sales tax on the refrigerator.
Solution:
Let the price of the refrigerator without sales tax be MP.
Here, the selling price SP = $ 17600
and the rate of sales tax, V%= 10%
Now, SP= MP + V% of MP
⟹ $ 17600 = MP + ¹⁰/₁₀₀ of MP
⟹ MP×¹¹⁰/₁₀₀ = $ 17,600
⟹ MP = $17,600
∴ the sale tax = Selling price - Printed price
= $ 17,600 - $ 16,000
= $ 1,600
5. If the rate of sale tax increases by 5%, the selling price of an article goes up by $ 40. Find the marked price of the article.
Solution:
Let the marked price be MP and rate of sale tax be V%.
∴ SP₁= MP + V% of MP
When the rate of sales tax increases by 5%,
the selling price = SP₂ + (V+5)% of MP.
Given,
SP₂-SP₁=$40
⟹ [SP₂+(V+5)% of MP] - [SP₂+V% of MP] = $ 40
⟹ 5% of MP= $ 40
⟹ ⁵/₁₀₀ ×MP= $ 40
⟹ MP= $ 40×20
⟹ MP= $ 800
∴ the marked price of the article is $ 800.
Examples 1
A bulb is sold out for Rs 226 at profit of 13%. At
what price was the bulb purchased?
Soln
S. P = Rs 226
Profit = 13%
C.P =?
S. P = C. P + profit
226 = C. P + 13% of C.P
C. P = Rs 200
Examples 2
The price of an article with 13% VAT Is Rs 1356.
Find the price of the article excluding VAT.
Solution
VAT = 13%
Price of article with 13% VAT = Price of article
without VAT + 13% of Price of article without
VAT
Or, 1356 = x+ 13% of x
x = Rs 1200
Examples 3
An article bought for Rs 450 is sold at a profit of
30% , what is selling price ?
Soln
C.P of the article = Rs 450
Profit = 30%
S.P = C.P + profit% of C.P
= 450 + 30% of 450
= Rs 585
Examples 4
The marked price of the radio is Rs 4000. If 20%
discount is given and some percentage of VAT
is imposed the price of the radio is Rs 3616.
Find the rate of VAT
soln
M.P = Rs 4000
Discount = 20%
S.P = M.P – discount
= 4000 - 20% 4000
= RS 3200
S. P with vat = 3200 + (VAT) x% of 3200
3616 =3200 + x% of 3200
416 = 32x
x = 13
∴ VAT% = 13%
Examples 5
The marked price of the cycle is Rs 3000. How
much should a customer pay if 10% discount and 13% VAT is allowed?
soln
M.P = Rs 3000
Discount = 10%
VAT = 10%
S. P = M.P - discount
=Rs 3000 - 10% of Rs 3000
= Rs 2700
S. P with VAT = Rs 2700 +13% of Rs 2700
= Rs 2700 + 13% * Rs 2700
= Rs 3051
Examples 6
A color T.V is sold at Rs 20,700 after 10%
discount with 15% VAT. Find the VAT amount.
Soln: