### Math - Class 5 - Profit and Loss / Application to Profit and Loss / Word Problems on Profit and Loss/ Determining Profit and Loss - Key Points/Notes/Worksheets/Explanation/Lesson/Practice Questions

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John is a shopkeeper. He buys goods from the wholesaler and sells them in his shop at a higher price to earn profit. When he succeeds in selling at higher price, he makes profit else he suffers loss.

__Let’s understand the concept in with following example:__If John buys sugar at rupees 50 per kg and sells at rupees 55 per kg, he makes profit of rupees (55 – 50 = 5) per kg. But due to some reason if he has to sell the sugar at rupees 48 per kg, he will make loss of (50 – 48 = 2) per kg.

__From the above example we understand__- The price at which John buys sugar is the Cost Price. Therefore, cost price is the price at which an item is purchased.

- The price at which John sells sugar is the Selling Price. Therefore, selling price is the price at which an item is sold.

- When S.P > C.P, he makes profit or gain, i.e. Profit or Gain = S.P – C.P

- When S.P < C.P, he suffer loss, i.e. Loss = C.P – S.P

- Charges such as transportation cost, labor cost, salary or wages paid, installation charge etc. are called expenses and these has to be added to the C.P to get actual profit.

- Profit% = Profit/C.P X 100

- Loss% = Loss/C.P X 100

__Example:__Tia’s boutique received rupees 5,000 from one client on Wednesday, but expenses came to rupees 2700. Here income is more than the expense. So, she earned profit of (5000-3700) = rupees 1300.On Thursday Tia received rupees 7,000 from other client and expenses came to rupees 7,700. Here income is less than the expense. So, she suffered the loss of (7,700-7,000) = rupees 700.

**Some more examples****Example 1**: Dia bought rice bag rupees 500 per bag. Due to spoilage, she had to sold them for rupees 450 per bag. Find the gain or loss%.**Solution:**Here, C.P = Rupees 500 per bagS.P = Rupees 450 per bag

As S.P < C.P, Therefore Dia suffer a loss.

Loss = C.P – S.P = 500 – 450 = Rupees 50 per bag

Loss% = Loss/C.P X 100 = 50/150 X 100 = 33.33%

**Example 2:**Mr Ravi bought a washing machine for rupees 15,000 and sold it for rupees 17,000. Find his profit or loss percent.**Solution:**Here, C.P = Rupees 15,000S.P = Rupees 17,000

As S.P > C.P, therefore Ravi made a profit.

Profit = S.P – C.P = 17,000 – 15,000 = Rupees 2000

Profit % = Profit/C.P X 100 = 2,000/15,000 X 100 = 13.33%

**Example 3:**Reena sold a carpet for rupees 10,000 at a profit rupees 2,000. Find the price at which she bought it.**Solution:**Here, S.P = 10,000Profit = 2,000

C.P = S.P - Profit

= 10,000 – 2,000

= Rupees 8,000

**Example 4:**Ravi has a Alto car worth rupees 2,50,000 and he wants to sell it at profit of rupees 50,000. What should car selling price be?**Solution:**Here, C.P = 2,50,000Profit = 50,000

S.P = C.P + Profit

= 2,50,000 + 50,000

= Rupees 3,00,000

**Example 5:**Sonu bought a laptop of rupees 1,50,000 at a loss of rupees 10,000. Find selling price of the laptop.**Solution:**Here, C.P = 1,50,000Loss = 10,000

S.P = C.P - loss

= 1,50,000 - 10,000

= Rupees 1,40,000

**Example 6:**Nimmi sold her television for rupees 30,000 at a loss of rupees 5,000.Find the cost price of the television.**Solution:**Here, S.P = 30,000Loss = 5,000

C.P = S.P + loss

= 30,000 + 5,000

= Rupees 35,000

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