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Thought-Process to Discover Knowledge

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Books and other education websites provide "matter-of-fact" knowledge. Instead, nubtrek provides a thought-process to discover knowledge.

In each of the topic, the outline of the thought-process, for that topic, is provided for learners and educators.

Read in the blogs more about the unique learning experience at nubtrek.

### Formulas for profit-loss-discount

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.

click on the content to continue..

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

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

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

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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