Students need not memorize 20+ formulas anymore for the topics profit-loss, discount, and tax.

`text(Profit%) = 100 xx` `(text(SalePrice)-text(CostPrice))``//text(CostPrice)`

`text(Discount%) = 100 xx` `(text(MarkedPrice)-text(SalePrice))``//text(MarkedPrice)`

`text(Tax%) = 100 xx` `(text(BilledPrice)-text(SalePrice))``//text(SalePrice)`

All these three formulas are very similar and has a simple explanation to the terms in numerator and denominator.

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Students are stressed by many formulas. This is listed for reference, but in the next pages, these are explained. *No need to memorize any of these.*

profit = sale price - cost price

loss = cost price - sale price

profit percentage = (sale price - cost price) * 100 / (cost price)

loss percentage = (cost price - sale price) * 100 / (cost price)

sale price = cost price * (100+profit%)/(100)

cost price = sale price * (100) / (100+profit%)

sale price = cost price * (100-loss%)/(100)

cost price = sale price * (100) / (100-loss%)

discount = marked price - sale price

discount percent = (marked price - sale price)*100 / marked price

sale price = markprice (100-discount%) / 100

marked price = sale price * 100 / (100- discount%)

tax = bill price - sale price

tax percent = (bill price - sale price)*100 / sale price

billprice = sale price (100+ tax%)/100

sale price = bill price * 100 /(100+tax%)

Summarizing all the terms learned so far.

• Shopkeeper buys a pen for `40` coins. (cost price)

• Shopkeeper spends `3` coins on transport or other shopkeeping expenses. (overhead expense)

• Shopkeeper marks the price of the pen as `60` coins. (marked price)

• Shopkeeper marks a `10` coins discount on the pen. (discount)

• Customer buys the pen for `50` coins (bill price). The bill price is given as inclusive of taxes.

• the shopkeeper pays `2` coins as tax (tax)

• the sale-price is `50-2 = 48` coins.

The profit for the shopkeeper

= marked price - discount - cost price - overhead expenses - tax

`= 60-10-40-3-2`

` = 5` coins (profit)

Summarizing all the terms learned with tax extra.

• Shopkeeper buys a pen for `40` coins. (cost price)

• Shopkeeper spends `3` coins on transport or other shopkeeping expenses. (overhead expense)

• Shopkeeper marks the pen as `60` coins. (marked price)

• Shopkeeper marks a `10` coins discount on the pen. (discount)

• Customer buys the pen for `50` coins (sale price). The sale price is given as excluding taxes.

• the customer pays `2` coins as tax (tax) to the shopkeeper. Effectively the customer pays `52` coins (bill price).

The profit for the shopkeeper

= marked price - discount - cost price - overhead expenses

`= 60-10-40-3 `

`= 7` coins (profit)

Note: The tax of `2` coins is collected from buyer and paid to government by the seller.

One need not memorize any formulas. Quickly follow through the *story* to recall formulas on the fly.

• Loss is the negative profit.

• Shopkeeper buys an article by cost price CP.

• Shopkeeper sells the article at sale price SP.

• Shopkeeper calculates the profit on the amount invested, which is cost price. So, profit percentage is given as percentage of cost price.*`text(Profit%) = 100 xx` `(text(SP)-text(CP))``//text(CP)` *

• shopkeeper adds a tag to the article as marked price MP.

• Discount is shown to the customer based on the price displayed to the customer, which is marked price. So, Discount percentage is given as percent of marked price.*`text(Discount%) = 100 xx` `(text(MP)-text(SP))``//text(MP)` *

• For the sale, government collects tax. Shopkeeper collects the tax on behalf of the government and submits the tax amount.

• Tax is added to the sale price in the bill and the total is called the billed price BP.

• Tax is paid by the customer on the amount taken by the seller, which is the sale price. So, the tax percentage is given as a percentage of sale price.*`text(Tax%) = 100 xx` `(text(BP)-text(SP))``//text(SP)` *

One need not memorize any formulas. Quickly follow through the *story* to recall formulas on the fly.

• Loss is the negative profit.

• Shopkeeper calculates the profit on the amount invested, which is cost price.*`text(Profit%) = 100 xx` `(text(SP)-text(CP))``//text(CP)` *

• Discount is shown to the customer based on the price displayed to the customer, which is marked price. *`text(Discount%) = 100 xx` `(text(MP)-text(SP))``//text(MP)` *

• Tax is paid by the customer on the amount taken by the seller, which is sale price. *`text(Tax%) = 100 xx` `(text(BP)-text(SP))``//text(SP)` *

The three formulas given above are easier to recall. Each has `3` variables and given any `2` quantities, use the equation as a linear equation (algebra) to solve for the third variable.

*Solved Exercise Problem: *

What is profit?

- money accepted in a sale
- sale price `-` cost price
- sale price `-` cost price

The answer is "sale price - cost price"

*Solved Exercise Problem: *

Profit percentage is given as a percent of which of the following?

Remember the shopkeeper makes the profit on the investment of "cost-price".

- sale price
- cost price
- cost price

The answer is "cost price"

*Solved Exercise Problem: *

Which of the following gives the formula for sale price?

- profit percent =`100 xx ` (SP-CP) `//` CP
- profit percent =`100 xx ` (SP-CP) `//` CP
- SP = CP `xx` profit percent

The answer is "profit percent =`100 xx ` (SP-CP) `//` CP"

*Solved Exercise Problem: *

A book is sold for `22` coins with `10%` profit included, what is the cost-price?

Which of the following is easier to solve the problem?

- memorize a formula of "cost-price = ..."
- substitute the given two in the known formula "profit percent = ..."
- substitute the given two in the known formula "profit percent = ..."

The answer is, substitute the given two in the known formula profit percent = ...

A book is sold for `22` coins with `10%` profit included, what is the cost-price?

Solution:

sale price = `22`

profit percentage = `10%`

profit percent =`100 xx ` (SP-CP) `//` CP

`10 = 100 xx (22-text(CP)) // text(CP))`

This is a linear equation of one variable. It is easy to solve this for cost price.

*Solved Exercise Problem: *

A book is sold for `22` coins with `10%` loss included, what is the cost-price?

Which of the following is easier to solve the problem?

- memorize a set of formulas for loss
- substitute the loss as negative profit in the known profit percentage equation
- substitute the loss as negative profit in the known profit percentage equation

The answer is "substitute the given two in the known formula profit percentage equation"

A book is sold for `22` coins with `10%` loss included, what is the cost-price?

Solution:

sale price = `22`

profit percentage = `-10%`

profit percent =`100 xx ` (SP-CP) `//` CP

`-10 = 100 xx (22-text(CP)) // text(CP))`

This is a linear equation of one variable. It is easy to solve this for cost price.

*Solved Exercise Problem: *

Discount percentage is given on which of the following?

Remember discount is shown to a customer and customer sees the mark-price on the article.

- sale price
- marked price
- marked price

The answer is "marked price"

*Solved Exercise Problem: *

Which of the following gives the formula for discount percentage?

- discount % `=100 xx` (MP-SP) `//`MP
- discount % `=100 xx` (MP-SP) `//`MP
- SP = MP `xx` discount percent

The answer is "discount % `=100 xx` (MP-SP) `//` MP".

*Solved Exercise Problem: *

A book is marked for `20` coins. The shop keeper sells for `16` coins. What is the discount percentage?

How to solve this problem?

- memorize a formula for "discount percent = ..."
- substitute the given information in the known formula " discount percent = ..."
- substitute the given information in the known formula " discount percent = ..."

The answer is "substitute the given information in the known formula : discount percent = ... "

A book is marked for `20` coins. The shop keeper sells for `16` coins. What is the discount percentage?

Solution:

marked price = `20`

sale price = `16`

discount % `=100 xx` (MP-SP) `//` MP

discount % `=100 xx (20-16) // 20`

This is a linear equation of one variable. It is easy to solve this for discount percent.

*Solved Exercise Problem: *

Tax percentage is calculate on which of the following?

Remember tax is paid by the customer on the amount taken by the shopkeeper.

- bill price
- sale price
- sale price

The answer is "sale price".

*Solved Exercise Problem: *

Which of the following gives the formula for tax percentage?

- tax % `= 100 xx` (BP-SP) `//` SP
- tax % `= 100 xx` (BP-SP) `//` SP
- BP = SP `xx` tax percent

The answer is "tax % `= 100 xx` (BP-SP) `//` SP"

*Solved Exercise Problem: *

A book is sold for `20` coins inclusive of `10%` tax. What is the sale price of the book?

How to solve this problem?

- memorize a formula for "sale price = ..."
- substitute the given information in the known formula "tax percent = ..."
- substitute the given information in the known formula "tax percent = ..."

The answer is "substitute the given information in the known formula"

A book is sold for `20` coins inclusive of `10%` tax. What is the sale price of the book?

Solution:

bill price = `20`

tax percent = `10%`

tax % `= 100 xx` (BP-SP) `//` SP

`10 = 100 xx (20-text(SP)) // text(SP)`

This is a linear equation of one variable. It is easy to solve this for sale price.

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