In this chapter, the use of “Rule of Fraction” is dominant. We should understand this rule very well because it is going to be used in almost all the questions

**Rule of Fraction**

If our required value is greater than the supplied value, we should multiply the supplied value with a fraction which is more than one. And if our required value is less than the supplied value, we should multiply the supplied value with a fraction which is less than one.

1). If there is a gain of X%, the calculating figures would be 100 and (100+X).

2). If there is a loss of Y%, the calculating figures would be 100 and (100-Y).

3). If the required value is more than the supplied value, our multiplying fractions should be 100+X/100 or 100/100-Y (both are greater than 1).

4). If the required value is less than the supplied value, our multiplying fractions should be 100/100+X or 100-Y/100 (both are less than 1).

**Cost price:**

The price, at which an article is purchased, is called its cost price. In short we write it as C.P.

**Selling price:**

The price, at which an article is sold, is called its selling price. In short we write it as S.P.

**Profit or Gain:**

When the selling price(SP) is greater than the cost price(CP) then it is a profit.

**SP > CP**

Profit= Selling Price(S.P) – Cost Price(C.P)

**Example:** If the selling price of a cloth is Rs.235 and the cost price of the same cloth is Rs. 200 then there is a profit of Rs.35.

**Loss:**

When the selling price(SP) is less than the cost price(CP) then is a loss.

**SP < CP**

Loss= Cost Price(C.P) – Selling Price(S.P).

**Example:** A trader bought a TV for Rs.12000 and sold it for Rs.10,000 then there is a loss of Rs.2000.

**Marked price:**

This is the price marked as the selling price on an article, also known as the listed price.

**List Price:**

List price is the price that is printed on the tag of the article. For all practical purposes, we consider it to be the same as the marked-price.

Margin: The profit percentage of the selling price is known as margin.

**Types Of Cost:**

**1. Fixed cost:**

It is a type of cost which is fixed under all conditions and does not vary according to the number of units produced.

**2. Variable cost:**

Variable cost is a type of cost which varies according to the number of units. This is quite easy to understand.

**3. Semi-variable cost:**

These costs are the ones that are fixed in part and variable in part. adequately, this is the case that we see most often. Imagine the scenario in a factory. There is a capital cost, which remains the same under all conditions and a variable cost of the product, which in turn depends upon various factors.

**Discount:**

Discount means decreasing the price offered on the marked or listed price.

**Some Important Points About Discount**

Regular price subtracted by Sale price gives the amount of discount.

If the discount is given in percent, then the amount of discount can be found by using the formula,

Amount of Discount = Regular Price × Rate of Discount.

**Example:**

Dev bought a laptop, which costs Rs.27000. But he was given a discount of RS.3000.

**Solution:**

Cost at which dev bought the laptop = Original cost of the laptop – Discount offered on the laptop

= Rs.27000 – Rs.3000 = Rs.24000

So, dev paid Rs.24000 for the laptop after discount.

**Profit %:**

Profit on Rs. 100 is called Profit %. Formula for Profit percentage

Profit % = *Profit*cost price x 100

**Loss %:**

Loss on Rs. 100 is called Loss %. Formula for Profit percentage

Loss % = *Loss *cost price x 100

**Overhead expenses:**

Sometimes, apart from paying the cost of an article, a shopkeeper has to spend money on transportation, labour, repair, . . . . such expenses are called overhead expenses.

Actual C.P of an article = Cost of article + Overhead expenses.

To find selling price (SP) when cost price (CP), gain % or loss % are given:

S.P = *(100 + gain%)*100 x CP

S.P = *(100 – loss%)*100 x CP

To find cost price (CP) when selling price (SP), gain % or loss % are given:

C.P = *100*(100 + gain%) x S.P

C.P = *100*(100 – loss%) x S.P

**Some quicker methods to solve the Questions:**

• If an article is sold at a gain of 10%, then SP = 110% of CP.

• If an article is sold at a loss of 10%, then SP = 90% of CP.

• If a seller claims that he is selling goods at cost price but uses false weight to earn profit

Profit% = *(True Weight – False Weight) x 100*False weight

• If there are two successive profits of X% and Y% in a transaction, the resultant profit is given by:

Resultant profit = *= (X + Y + XY)*100

• If there is a profit of X% and loss of Y% in a transaction, the resultant profit or loss is given by:

Resultant profit = *(X + Y – XY)*100

**Practise Problems Related To This Topic**

▪ If C.P of x article is equal to the selling price of y articles then the, then

Resultant profit % or loss % = *(y − x)*y× 100

**1). Find the cost price of an article which is sold for Rs. 220 at a loss of 12%.**

**Solution:**

In this question:

S P = Rs. 220,

loss =12%.

**C.P = 100(100 – loss%) x S.P**

C.P =

*100*(100 – 12) x 220

C.P =

*100*88 x 220 = 250

Therefore,

cost price = Rs. 250. rupees 250.

**2). A person incurs 5% loss by selling a watch for Rs 1140. At what price should the watch be sold to earn 5% profit?**

**Solution:**

Let the new S.P. be RsX,

Then,Ist SP = (100 – loss percentage)

IInd SP = (100 + Gain percentage)

We can write:

*(100 – 5)*1140 =

*(100 + 5)*X

*95*1140 =

*105*X

95X = 105 x 1140

Hence, simplify this: X =

*(105 × 1140)*95 = Rs. 1260. Therefore,

we can say that the new S P = Rs. 1260

**3). saurav sell an article at a discount of 80% and get a profit of 60% on that article to calculate the mark up over the cost price?**

**Solution:**

Let us assume that ….

Cost Price = Rs 100.

So, Selling Price = Rs 160.

Now, after giving a discount of 80% over MP, Rs 160 is the SP.

Let the Marked Price: X

SP = 20% of X

160 = 20% of X

X = 800

% Mark Up = (700/100) × 100 = 700 %.

**4). Sneha and Saurav sell some article for Rs 8000 each. sneha calculates her profit percent on his CP and Saurav calculates his profit percent wrongly on SP. What is the difference in their actual profit if both claims to have a profit of 60%?**

**Solution:**

For sneha

SP = Rs 8,000

**Profit % =**

*Profit*cost price x 100Profit = 60% of CP

CP = Rs 5000

Profit = Rs 3000

For saurav

SP = Rs 8,000

Profit = 60% of SP = 60% of 8000 = 4800

CP = Rs 3,200

Profit = Rs 4800

So, the difference in profit = Rs 1800

**5). James and Jiya sold two articles at Rs 12,000 each. One is sold at a profit of 20% and another one at a loss of 20%. What is the net loss?**

**Solution:**

For article-1

SP = Rs 12,000

gain% = 20

**C.P =**

*100*(100 + gain%) x S.PC.P =

*100*(100 + 20) x 12,000

=

*100*120 x 12,000

CP = Rs 10,000

For article-2

SP = Rs 12,000

loss% = 20

**C.P =**

*100*(100 – loss%) x S.PC.P =

*100*(100 – 20) x 12,000

=

*100*50 x 12,000

CP = Rs 15,000

So, total CP = Rs 25,000 and total SP = Rs 24,000

**Loss= Cost Price(C.P) – Selling Price(S.P).**

So, loss = 25,000 – 24,000 = Rs 1,000.

**6). A bottle is purchased for Rs. 80 and is sold for Rs. 65. What is his profit or loss in Rs?**

**Solution:**

As given CP = 80, SP = 65.

**Profit = SP – CP**

⇒ 65 – 80 = Rs. – 15.

**7). The MRP of a article is 60% above its manufacturing cost. The article is sold through a retailer, who earns 19% profit on his purchase price. What is the approx. profit percentage for the manufacturer who sells his article to the retailer? The retailer gives 15% discount on MRP.**

**Solution:**

Assume manufacturing cost = 100 and

manufacturer profit = x

Maximum Retail Price (MRP) of a product is 60% above its manufacturing cost,

MRP = 160% of 100 = 160

The retailer gives 15% discount on MRP.

So, customer price is 85% of MRP.

Buyer Price = 85% of 160 = 136

The manufacturer makes X rupees profit, and then the retailer makes 19% profit.

So, 119% of (100 + X) = 136

⇒ 119 (100 + X) = 13600

⇒ (100 + X) = 114.28

⇒ X= 14.28

Hence, Manufacturer profit = 14.2%

**8). An Article costs Rs. 5000 and it is marked up 40% by the shopkeeper. A customer walks into the shop and seems really interested in the article. Sensing this, the shopkeeper gets greedy and he raises the markup % to 80% and gives a discount of 20% to the customer. How much more/less money would he had made, had he not gotten greedy?**

**Solution:**

1st outline: When markup was 40%

= 140% of 5000 = 7000

2nd outline: When there is markup of 80 % and then a discount of 20%

= 80% of 180% of 5000 = 7200

In the second scenario, he is earning Rs. 200 less.

earning Rs. 200 less.

**9). A firm of readymade garments makes both men’s and women’s shirts. Its average profit is 5% of the sales. Its profit in men’s shirts average 9% of the sales and women’s shirts comprise 60% of the output. The average profit per sale rupee in women shirts is???**

**Solution:**

Let the total sales be Rs. 100

Women’s shirt comprise 60% of the output

Rs. 60 out of Rs. 100 is sales of female’s shirts

Men’s shirts comprise (100 – 60) = 40% of the output

Rs. 40 out of Rs. 100 is the sales of male’s shirts

Average profit from men’s shirt = 9% of 40 = Rs. 3.6

Overall average profit = 5 % of 100 = Rs. 5

Average profit from women’s shirts = 5 – 3.6 = Rs. 1.4

From the sale of Rs. 60

The profit per rupee is 1.4/60 = 0.0233

The average profit per sale rupee in women shirts is Rs. 0.0233

**10). Aditi and Sumit sold their bats at Rs. 5457 each but Aditi incurred a loss of 15%, while Sumit gained 2%. What is the ratio of the cost price of the bat of Aditi to that of Sumit?**

**Solution:**

S.P = Rs. 5457

CP of Aditi’s bat

loss = 15%

we know,

**C.P =**

*100*(100 – loss%) x S.PC.P =

*100*(100 – 15) x 5457

C.P =

*100*85 x 5457

=

*(5457 x 100)*85

=

*(5457 x 20)*17

= 321 x 20= Rs.6420

CP of Sumit’s bat

gain = 2%

we know,

**C.P =**

*100*(100 + gain%) x S.PC.P =

*100*(100 +2) x 5457

C.P =

*100*102 x 5457

=

*(5457*100)*102 =

*(5457*50)*51

107 x 50= Rs.5350

Then, the required ratio is = 6420:5350=642:535= 6:5

I hope, this article will help you a lot to understand the **Profit, Loss And Discount**. If you still have any doubts and problems with any topic of mathematics you can ask your problem in the Ask Question section. You will get a reply shortly.