## Class 10 Mathematics Note

# Profit and Loss

**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

Profit % = $\frac{{{\rm{profit}}}}{{{\rm{C}}.{\rm{P}}}}{\rm{\: \: }}$* 100%

If the selling price of the article is less than its cost price, it is called loss

i.e S.P < C.P

Profit = C.P – S.P

Loss % = $\frac{{{\rm{Loss\: }}}}{{{\rm{C}}.{\rm{P}}}}{\rm{\: \: }}$* 100%

**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

Or, Discount = M.P – S.P

Discount % = $\frac{{{\rm{discount\: amount\: }}}}{{{\rm{M}}.{\rm{P\: \: }}}}{\rm{*}}100{\rm{\% \: }}$

**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.

** Examples 1**

A bulb is sold out for Rs 226at 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 = $32$ x

X = 13%

∴ VAT% = 13%

**Examples 5**

The marked price of the cycle is Rs 3000. How much should a customer pa if 10% discount and 13% VAT is allowed?

soln

M.P = Rs 3000

Discount = 10%

VAT = 10%

S. P = M.P - discount

= 3000 - 10% of 3000

= 2700

S. P with VAT = Rs 2700 +13% 2700

= 2700 + 13% *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:

Let the Marked Price be x. Then,

SP = x – 10%of x

= ${\rm{x}} - \frac{{10}}{{100}}{\rm{x}}$

= $\frac{{9{\rm{x}}}}{{10}}$

Again, after VAT is added,

SP’ = $\frac{{9{\rm{x}}}}{{10}} + 15{\rm{\% *}}\frac{{9{\rm{x}}}}{{10}}$

Or, 20,700 = $\frac{{9{\rm{x}}}}{{10}} + \frac{{15}}{{100}}{\rm{*}}\frac{{9{\rm{x}}}}{{10}}$

Or, 20,700 = $\frac{{9{\rm{x}}}}{{10}} + \frac{{135{\rm{x}}}}{{1000}}$

Or, $20,700 = \frac{{900{\rm{x}} + 135{\rm{x}}}}{{1000}}$

Or, 20700000 = 1035x

So, x = Rs. 20,000

Now, SP = $\frac{{9{\rm{*}}20,000}}{{10}}$ = 18,000

So, VAT = 20,700 – 18,000

= Rs. 2,700