WORD PROBLEMS ON PROFIT AND LOSS

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Word problems on profit and loss

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%

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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.

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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)