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**Problem 1 :**

A man buy an article for $27.50 and sells it for $28.60. Find his profit percent.

**Problem 2 :**

If a camera is purchased for $490 and sold it for $465.50, find the loss percent.

**Problem 3 :**

By selling 33 meters of cloth, one gains the selling price of 11 meters. Find the profit percent.

**Problem 4 :**

A person incurs 5% loss by selling a laptop for $1140. At what price should the laptop be sold to earn 5% profit ?

**Problem 5 :**

The cost price of 21 articles is equal to S.P of 18 articles. Find the profit or loss percent.

**Problem 6 :**

A man bought candies at 3 for a dollar. How many for a dollar must he sell to earn a profit of 50% ?

**Problem 7 :**

If the cost price is 96% of the selling price, then what is the profit percent ?

**Problem 8 :**

An article is sold at a certain price. By selling it at 2/3 of that price, one loses 10%. Find the profit percent at original price.

**Problem 1 :**

A man buy an article for $27.50 and sells it for $28.60. Find his profit percent.

**Solution :**

**Given :**

Cost price = $27.50

Selling price = $28.60

**Finding Profit : **

Profit = Selling price - Cost price

Profit = 28.60 - 27.50

Profit = 1.10

**Finding Profit Percent : **

Profit percent = (Profit/Cost price) ⋅ 100 %

Profit percent = (1.10/27.50) ⋅ 100 %

Profit percent = 4 %

**Problem 2 :**

If a camera is purchased for $490 and sold it for $465.50, find the loss percent.

**Solution :**

**Given : **

Cost price = $490

Selling price = $465.50

**Finding Loss : **

Loss = Cost price - Selling price

Loss = 490 - 465.50

Loss = 24.50

**Finding Loss Percent : **

Loss percent = (Loss/Cost price) ⋅ 100 %

Loss percent = (24.50/490) ⋅ 100 %

Loss percent = 5 %

**Problem 3 :**

By selling 33 meters of cloth, one gains the selling price of 11 meters. Find the profit percent.

**Solution :**

Let the selling price of 1 meter of cloth be $1.

Then, the selling price of 33 meters of cloth = $33

By fact, we have

S.P of 33 m - C.P of of 33 m = Profit

**Given : **

By selling 33 meters of cloth, the profit earned is the selling price of 11 meters.

So, we have

S.P of 33 m - C.P of of 33 m = S.P of 11 m

S.P of 33 m - S.P of of 11 m = C.P of 33 m

S.P of 22 m = C.P of 33 m

22 ⋅ 1 = C.P of 33 m

22 = C.P of 33 m

**Finding Profit :**

Profit = Selling price - Cost price

Profit = 33 - 22

Profit = 11

**Finding Profit Percent : **

Profit percent = (Profit/Cost price) ⋅ 100 %

Profit percent = (11/22) ⋅ 100 %

Profit percent = (1/2) ⋅ 100 %

Profit percent = 50 %

**Problem 4 :**

A person incurs 5% loss by selling a laptop for $1140. At what price should the laptop be sold to earn 5% profit ?

**Solution :**

Let "x" be the cost price of the laptop.

**Given : **

The laptop is sold for $1140 at 5% loss.

So, we have

(100 - 5)% of x = 1140

95% of x = 1140

0.95x = 1140

Divide both sides by 0.95

0.95x / 0.95 = 1140 / 0.95

x = 1200

The cost price of the laptop = $1200.

Selling price of the laptop at 5% proft is

= (100 + 5)% of 1200

= 105% of 1200

= 1.05 ⋅ 1200

= 1260

Hence, the laptop should be sold at $1260 to earn a profit of 5%.

**Problem 5 :**

The cost price of 21 articles is equal to S.P of 18 articles. Find the profit or loss percent.

**Solution :**

Let the cost of 1 article $1.

Then, the cost price of 18 articles = $18

**Given :**

Cost price of 21 articles = Selling price of 18 articles

21 ⋅ 1 = Selling price of 18 articles

21 = Selling price of 18 articles

**Finding Profit :**

Profit = S.P of 18 articles - C.P of 18 articles

Profit = 21 - 18

Profit = 3

**Finding Profit Percent : **

Profit percent = (Profit/Cost price) ⋅ 100 %

Profit percent = (3/18) ⋅ 100 %

Profit percent = (1/6) ⋅ 100 %

Profit percent = 100/6 %

Profit percent = 16 ⅔ %

**Problem 6 :**

A man bought candies at 3 for a dollar. How many for a dollar must he sell to earn a profit of 50% ?

**Solution :**

Cost price of 3 candies = $1

Selling price of 3 candies at 50% is

= (100 + 50)% of cost price of 3 candies

= 150% of 1

= 1.5 ⋅ 1

= 1.5

So, he has to sell 3 candies for $1.50 to earn a profit of 50%.

Selling price of 1 candy = 1.50/3

Selling price of 1 candy = $0.50

No. of candies he has to sell for a dollar is

= 1/0.50

= 2

Hence, the person must sell 2 candies for a dollar to earn a profit of 50%.

**Problem 7 :**

If the cost price is 96% of the selling price, then what is the profit percent ?

**Solution :**

Let the selling price be $100.

Then the cost price is $96.

**Finding Profit :**

Profit = Selling price - Cost price

Profit = 100 - 96

Profit = 4

**Finding Profit Percent : **

Profit percent = (Profit/Cost price) ⋅ 100 %

Profit percent = (4/96) ⋅ 100 %

Profit percent = (1/24) ⋅ 100 %

Profit percent = 4.17 %

**Problem 8 :**

An article is sold at a certain price. By selling it at 2/3 of that price, one loses 10%. Find the profit percent at original price.

**Solution :**

Let the original selling price be $3 and the cost price be x.

(Here, original selling price is assumed as $3, because when it is multiplied by 2/3, the result will be an integer)

Then, 2/3 of the original selling price is

= 2/3 ⋅ 3

= 1

Selling price at 10% loss = 2/3 of the original S.P

(100 - 10)% of cost price = 2

90% of "x" = 2

0.9 ⋅ x = 2

0.9x = 2

Divide both sides by 0.9

0.9x / 0.9 = 2 / 0.9

x = 20/9

So, the cost price = $20/9.

**Finding Profit :**

Profit = Selling price - Cost price

Profit = 3 - 20/9

Profit = 27/9 - 20/9

Profit = (27 - 20)/9

Profit = 7/9

**Finding Profit Percent : **

Profit percent = (Profit/Cost price) ⋅ 100 %

Profit percent = [(7/9) / (20/9)] ⋅ 100 %

Profit percent = (7/9) ⋅ (9/20) ⋅ 100 %

Profit percent = 35 %

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