"Profit and loss" is the much required stuff for the people who are preparing for competitive exams.

Using the hints given on this web page on profit & loss and pdf document, we can solve any word problem on profit & loss.

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Let us go through the hints one by one.

**Hint 1 : **

**Cost price and profit percentage are given. **

**Cost price = C.P, Profit percentage = P%**

**Then Selling price (S.P) = (100+P)% x C.P**

**Hint 2 : **

**Cost price and loss percentage are given. **

**Cost price = C.P, Loss percentage = L%**

**Then Selling price (S.P) = (100 - L)% x C.P**

**Hint 3 : **

**Profit = S.P - C.P**

**Loss = C.P - S.P**

**Hint 4 : **

**Cost price and Profit are given**

**Cost price = C.P, Profit = "K"**

**Hint 5 : **

**Cost price and Loss are given**

**Cost price = C.P, Loss = "K"**

**Hint 6 :**

**Selling price and profit percentage are given.**

**How to find cost price ?**

**Use "Hint 1" and solve for C.P **

**Hint 7 : **

**Selling price and loss percentage are given.**

**How to find cost price ?**

**Use "Hint 2" and solve for C.P **

**Hint 8 : **

**Marked Price : It is the price before discount given**

**Selling price = Marked price - Discount value**

**Hint 9 : **

**Marked price = M.P, Discount = D%**

**Then, Discount value = (D% ) x M.P**

** Selling price (S.P) = (100 - D)% x M.P **

**Hint 10 : **

**Marked price (M.P) and discount value are given.**

**Then shortcut to find the discount percentage is, **

**Hint 11 : **

**RETAILER USING FALSE WEIGHT : **

**A trader cheats his customer to make
a profit by stating that he sells at cost price.But he gives his
customer less than 1000 grams (false weight) for every kg.
**

**Cheated value = Original weight - False weight**

**Then shortcut to find profit percentage is, **

**Hint 12 : **

**Hint 13 :**

**Problem 1 :**

A trader cheats his customer to make a profit by stating that he sells at cost price but gives his customers only 800 grams. for every 1000 grams. What is his profit percentage?

**Solution :**

Cheated Value = 1000 - 800 = 200

False weight = 800

Profit % = (Cheated value/False weight)x100%

Profit % = (200/800)x100%**Profit % = 25%**

Let us look at the next problem on "Word problems on profit and loss"

**Problem 2 :**

A sells to B an item at 15% profit. B sells the same item to C at 20% profit. If C pays $ 1656 for it. What is the price at which A bought the item?

**Solution :**

**Hence, the price at which A bought the item is $1200 **

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**Problem 3 :**

Mr. Lenin sold a chair at a loss of 15%. If he had sold at a profit of 10%, he would have got $100 more. What is the cost is the cost price of the chair?

**Solution :**

Let "x" be the cost price of the chair

S.P (-15%) = 85% of x

= 0.85x --------(1)

S.P (+10%) = 110% of x

= 1.1x ---------(2)

In (2), he got $100 more than (1). So we have

(2) - (1) = 100

1.1x - 0.85x = 100

0.25x = 100

25x = 10000

x = 400

**Hence, the cost price of the chair is $400**

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**Problem 4 :**

If
good are purchased for $ 1500 and one fifth of them sold at a loss of
15%. Then at what profit percentage should the rest be sold to obtain a
profit of 15%?

**Solution :**

As per the question, we need 15% profit on $1500.

Selling price for 15% on 1500

S.P =115% x 1500 = 1.15x1500 = **1725**

**When all the good sold, we must have received $1725 for 15% profit.**

When we look at the above picture, in order to reach 15% profit overall, the rest of the goods ($1200) has to be sold for $1470.

That is,

C.P = $1200, S.P = $1470, Profit = $270

Profit percentage = (270/1200) x 100

Profit percentage = 22.5 %

**Hence, the rest of the goods to be sold at 22.5% profit in order to obtain 15% profit overall.**

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**Problem 5 :**

By selling 20 articles, a trader gained the selling price of 5 articles. Find the profit percent.

**Solution :**

Let "X" be the S.P of 5 articles.

Given : Profit of 20 articles = S.P of 5 articles

So, **profit of 20 articles = X**

S.P of 20 articles = 4 . (S.P of 5 articles) = 4X

C.P of 20 articles = S.P of 20 articles - Profit of 20 articles

C.P of 20 articles = 4X - X

**C.P of 20 articles = 3X**

Profit percentage = (X / 3X).100% = (1/3).100%

Profit percentage = 33.33%

**Hence, the profit percentage is 33.33**

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**Problem 6 :**

I purchased 120 books at the rate of $3 each and sold 1/3 of them at the rate of $4 each. 1/2 of them at the rate of $ 5 each and rest at the cost price. Find my profit percentage.

**Solution :**

Total money invested = 120x3 = $360 -------(1)

Let us see, how 120 books are sold in different prices.

From the above picture,

Total money received = 160 + 300 +60 = $ 520 --------(2)

Profit = (2) - (1) = 520 - 360 = $160

Profit percentage = (160/360)x100 % = 44.44%

**Hence the profit percentage is 44.44**

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**Problem 7 :**

A trader marks his goods 20% above the cost price and allows a discount of 10% for cash. Find the profit percentage

**Solution :**

Let the cost price be $100.

Then, marked price (M.P) = $120

Let the selling price be "X"

From the above picture, we get

90% of (M.P) = X

(0.9).120 = X

108 = X --------> S.P = 108

Cost price = $100, Selling Price = $108 ---------> **Profit % = 8%**

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**Problem 8 :**

A
person wants to get 20% profit after selling his object at 20%
discount. Find the required percentage increase in marked price.

**Solution :**

Let the cost price be $100.

Then, the selling price = $120

Let the marked price be "X"

From the above picture, we get

80% of (M.P) = S.P

(0.8)X = 120

X = 150 --------> M.P = 150

Cost price = $100, Marked Price = $150

**Hence, the required percentage increase = 50%**

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**Problem 9 :**

A
person buys 8 articles for $15 and sells them at 10 for $18. Find the profit or loss percentage.

**Solution :**

**Cost price : **

8 articles -------> $15

40 articles = 5 x 8 articles = 5x15 = $75

**C.P of 40 articles = $75 ----------(1)**

**Selling price :**

10 articles -------> $18

40 articles = 4 x 10 articles = 4(18) = $72

**S.P of 40 articles = $72 ----------(2)**

From (1) and (2), we get C.P > S.P.

So there is loss.

And loss = (1) - (2) = 75 - 72 = 3

Loss percentage = (3/75)x100 % = 4%

**Hence, the loss percentage is 4. **

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**Problem 10 :**

The selling price of 10 articles is the cost price of 15 articles. Find profit or loss percentage.

**Solution :**

Let the cost price of one article be $1 -------(1)

**Given : **

S.P of 10 articles = C.P of 15 articles

S.P of 10 articles = 15x1 = $15

S.P of one article = 15/10 = $1.5 -------(2)

From (1) and (2), we get S.P > C.P

So, there is profit.

Profit = (2) - (1) = 1.5 - 1 = 0.5

Profit percentage = (0.5/1)x100 = 50%

**Hence, the profit percentage = 50%**

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**Problem 11 :**

Sum of the cost price of two products is $50. Sum of the selling price of the same two products is $52. If one is sold at 20% profit and other one is sold at 20% loss, find the cost price of each product.

**Solution :**

Let "x" and "y" be the cost prices of two products.

Then, x + y = 50 --------(1)

Let us assume thatr "x" is sold at 20% profit

Then, the selling price of "x" = 120% of "x"

selling price of "x" = 1.2x

Let us assume thatr "y" is sold at 20% loss

Then, the selling price of "y" = 80% of "y"

selling price of "x" = 0.8y

Given : Selling price of "x" + Selling price of "y" = 52

1.2x + 0.8y = 52 -------> 12x + 8y = 520

3x + 2y = 130 --------(2)

Solving (1) and (2), we get x = 30 and y = 20

**Hence the cost prices of two products are $30 and $20.**

**Let us look at the next problem on "Word problems on profit and loss"**

**Problem 12 : **

A computer store used a markup rate of 40%. Find the selling price of a computer game that cost the retailer $25.

**Solution : **

Selling price (S.P) = (100+M)% x C.P

Here, M = 40, C.P = $25

Then, S.P = (100 + 40)% x 25

S.P = 140% x 25

S.P = 1.4 x 25 = $35

**Hence, the selling price is $35**

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**Problem 13 : **

A golf store pays its wholesaler $40 for a certain club, and then sells it to a golfer for $75. What is the markup rate?

**Solution : **

Cost price (C.P) = $ 40

Selling price (S.P) = $ 75

Mark up value = 75 - 40 = $ 35

Mark up rate = (35/40)x100 % = 87.5 %

**Hence, the mark up rate is 87.5 %**

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**Problem 14 : **

A store uses a 40% markup on cost. Find the cost of a pair of shoes that sells for $63.

**Solution : **

Selling price (S.P) = (100+M)% x C.P ---------(1)

Here, S.P = $ 63, M = 40

Plugging the above values in (1)

(1)-----------> 63 = (100+40)% x C.P

63 = 140% x C.P ---------> 63 = 1.4 x C.P

63/1.4 = C.P ---------> 45 = C.P

**Hence, the cost of a pair of shoes is $ 45**

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**Problem 15 : **

A product is originally priced at $55 is marked 25% off. What is the sale price?

**Solution : **

Selling price (S.P) = (100 - M)% x L.P ---------(1)

Here, L.P = $ 55, M = 25

Plugging the above values in (1)

(1)-----------> S.P = (100 - 25)% x 55

S.P = 75% x 55 ---------> S.P = 0.75 x 55

S.P = 41.25

**Hence, the selling price is $ 41.25**

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**Problem 16 : **

A product that regularly sells for $425 is marked down to $318.75. What is the discount rate?

**Solution : **

Regular price = $ 425

Marked down price = $ 318.75

Marked down value = 425 - 318.75 = 106.25

Marked down rate = (106.25 / 425) x 100 %

Marked down rate = 25 %

**Hence, the marked down rate is 25 %**

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**Problem 17 : **

A product is marked down 15%; the sale price is $127.46. What was the original price?

**Solution : **

Selling price (S.P) = (100 - M)% x Original price ---------(1)

Here, S.P = 127.46, M = 15

Plugging the above values in (1), we get

127.46 = (100 - 15) x Original price

127.46 = 85% x Original price

127.46 = 0.85 x Original price

127.46 / 0.85 = Original price

149.95 = Original price

**Hence, the original price is $ 149.95**

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**Problem 18 :**

On selling 20 units of an item, the profit is equal to cost price of 5 units. Find the mark mark up rate.

**Solution :**

Let "m" be the cost price of one unit.

Then, the cost price of 20 units = 20m

Profit on selling 20 units = C.P of 5 units = 5m

Mark up rate = ( profit / cost ) x 100 %

= (5m / 20m) x 100 %

= 25%

**Hence, the mark up rate is 25%**

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**Problem 19 :**

On selling an item, a trader gets a profit of $20. If the selling price is five times the profit, find the mark up rate.

**Solution :**

Profit = $20

Selling price = 5 x profit = 5 x 20 = $100

Cost price = Selling price - Profit

Cost price = 100 - 20 = $80

Mark up rate = ( profit / cost ) x 100 %

= (20 / 80) x 100 %

= 25%

**Hence, the mark up rate is 25%**

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**Problem 20 :**

Difference between the cost price of two products is $10. Difference between the selling price is $20. If one is sold at 20% profit and other one is sold at 20% loss, find the cost price of each product.

**Solution :**

Let "x" and "y" be the cost prices of two products.

Then, x - y = 10 --------(1)

Let us assume thatr "x" is sold at 20% profit

Then, the selling price of "x" = 120% of "x"

selling price of "x" = 1.2x

Let us assume thatr "y" is sold at 20% loss

Then, the selling price of "y" = 80% of "y"

selling price of "x" = 0.8y

Given : Selling price of "x" - Selling price of "y" = 12

1.2x - 0.8y = 20 -------> 12x - 8y = 200

3x - 2y = 50 --------(2)

Solving (1) and (2), we get x = 30 and y = 20

**Hence, the cost prices of two products are $30 and $20.**

Here we have have listed out all the shortcuts which are required to solve profit and loss problems. Students can solve any word problem on profit and loss using the shortcuts which have been explained above.

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