A Person can gain profit only if Selling Price > Cost Price. Also, a person generates loss when Selling Price < Cost Price. So let’s understand each term in detail.

**Selling Price **(S.P)

**Definition: **The price at which a shopkeeper sells an item to a customer is known as the Selling price(S.P).

**Formula: **To calculate the selling price(S.P) when the (profit/cost) % is known:

Selling Price (S.P) = { [ ( 100 + Profit ) / 100 ] * C.P }

Selling Price (S.P) = { [ ( 100 – Loss) / 100 ] * C.P }

### Cost Price (C.P)

**Definition: **The price at which a shopkeeper bought an item from a seller is known as the Cost price(C.P).

**Formula**: To calculate cost price(C.P) when the (profit/cost) % is known:

Cost Price (C.P) = { [ 100 / (100 + Gain ) ] * S.P }

Cost Price (C.P) = { [ 100 / (100 – Loss ) ] * S.P }

### Profit

**Definition: **If the amount for which an item is sold is more than the amount at which that particular item is bought is called Profit.

**Formula: **

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

### Loss

**Definition:** If the amount for which an item is sold is less than the amount at which that particular item is bought is called Loss.

**Formula:**

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

**Profit Percentage **

**Formula: **

Profit % = [ ( Profit * 100 ) / C.P ]

### Loss Percentage

**Formula: **

Loss % = [ ( Loss * 100 ) / C.P ]

### Selling Price(S.P) when Cost Price(C.P) & Gain % Or Loss % are given

**Formula: **

S.P when C.P and Gain % are given:

= [ (100 + Gain % ) / 100 * C.P ]

S.P when C.P and Loss% are given:

= [ (100 – Loss% ) / 100 * C.P ]

### Cost Price(C.P) when Selling Price(S.P) & Gain % Or Loss % are given

**Formula:**

C.P when S.P and Gain % are given:

= [ 100 / ( 100 + Gain % )* S.P ]

C.P when S.P and Loss% are given:

= [ 100 / ( 100 – Loss % )* S.P ]

## Examples

**Example 1. A Student buys a book for ₹ 600 and sells it for ₹ 700. Find his gain and gain percent.**

**Solution:**

Given, Cost Price of book = ₹ 600

Selling Price of book = ₹ 700

By using the gain formula,

Gain= Selling Price – Cost Price= 700 – 600

=

₹ 100

By using the gain% formula,

Gain%= (gain/cost price) * 100= (100/600) * 100

= 100/6

=

16.66%

**Example 2. Sonia purchased a car for ₹ 450000. She used it for three months and then sold it for ₹ 435000. Find her loss percent?**

**Solution:**

Given, C.P = ₹ 450000 and S.P = ₹ 435000

∴ Loss = C.P – S.P

= ₹ ( 450000 – 435000 )

= ₹ 15000

Loss % = [ ( Loss / C.P ) * 100 ] %

= [ ( 15000 / 450000 ) * 100 ] %

= 10/3 %

So, the loss percent = 10/3 %

**Example 3. Sneha purchased a bicycle for ₹ 3500 and spent ₹ 1000 on its repair. She sold it at a gain of 40%. For how much did she sell the bicycle?**

**Solution:**

Total cost price of the bicycle = price paid to purchase it + Repair charges

C.P = ₹ (3500 + 1000) = ₹ 4500

S.P = [ (100 + Gain % ) / 100 * C.P ]

= [ ( 100 + 40 ) /100 * ₹ 4500 ]

= ₹ 140/100 * 4500

= ₹ 6300

So, Sneha sold the bicycle for ₹ 6300

**Example 4. A merchant lost 8% by selling an iPod for ₹12880. At what price should he sell if in order to gain 8%?**

**Solution:**

S.P of the iPod = ₹12880 , Loss % = 8%

C.P of the iPod = [ 100 / ( 100 – Loss % ) * S.P ]

= [ ( 100 / 100 – 8 ) * ₹12880 ]

= ₹ 100 / 92 * 12880 = ₹ 14000

Now, C.P = ₹14000, Gain % = 8%

S.P of the iPod = [ (100 + Gain % ) / 100 * C.P ]

= [ ( 100 + 8 ) / 100 * ₹14000

= ₹ ( 108 / 100 ) * 14000

= ₹15120

So, he should sell the iPod at ₹15120 to gain a profit of 8%.

**Example 5**.** A man bought goods worth ₹ 4500 and sold 1/3 of the goods at a loss of 10 %. At what gain percent should he sell the remaining goods so as to gain 20% on the whole transaction?**

**Solution:**

C.P of goods = ₹ 4500, Gain = 20%

S.P of goods = [ (100 + Gain % ) / 100 * C.P ]

= [ ( 100 + 20 ) / 100 * ₹ 4500

= ₹ 120/100 * 4500

= ₹ 5400

C.P of 1/3 of the goods = ₹ (1/3 * 4500 ) = ₹ 1500

∴ S.P of 1/3 of the goods at a loss of 10%

= [ (100 – Loss% ) / 100 * C.P ]

= [ ( 100 – 10 ) /100 * ₹ 1500 ]

= ₹ 90/100 * 1500 = ₹ 1350

∴ S.P of the remaining goods = S.P of all the goods – S.P of 1/3 of the goods

= ₹ 5400 – ₹ 1350 = ₹ 4050

∴ C.P of the remaining goods = C.P of all the goods – C.P of 1/3 of the goods

= ₹ 4500 – ₹ 1500 = ₹ 3000

Gain = S.P – C.P

= ₹ 4050 – ₹ 3000 = ₹ 1050

Gain % = ( Gain /C.P ) * 100% = ( 1050/3000 ) * 100% = 35%

So, The man should sell the remaining goods at a gain of 35%.

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