"Markup and markdown word problems answers" is an important category of percentage problems.

First let us understand what is mark up and mark down.

**Mark up ----> Increasing **

**To get profit in a business, a trader increases the cost price and sells the product. This increment in price is called as "Mark up" **

**This "Mark up can either be in percent or in dollars. **

**Mark Down ----> Decreasing**

**To increase the sale, stores will decrease the price of a product by giving offer or discount. This offer or discount is called as "Mark down". **

**This mark down can either be in percent or in dollars. **

To do mark up and mark down word problems answers, let us go through the hints related to "Markup and Mark down"

**Hint 1 :**

**Cross price and marked up percentage are given.**

**Cost price = C.P, Marked up percentage = M %**

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

**Hint 2 :**

**List price and marked down percentage are given.**

**List price = L.P, Marked down percentage = M %**

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

**Hint 3 :**

**List price price and marked down value (in dollars ) are given. **

**List price = L.P, Marked down value = $M**

**Then, mark down rate = ( M / L.P ) x 100 %**

**Hint 4 :**

**Cost price and marked up value are given**

**Cost price = C.P, Marked up value = $M**

**Then, mark up rate = ( M / C.P ) x 100 % **

**Hint 5 :**

**Cost price and selling price are given. **

**Cost price = C.P, Selling price = S.P and S.P > C.P**

**So, Gain = S.P - C.P **

**Then, mark up rate = ( Gain / C.P ) x 100 %**

To have better understanding on "Markup and markdown word problems answers", let us look at some examples.

**Example 1 : **

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**

Let us look at the next example on "Markup and markdown word problems answers"

**Example 2 : **

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 %**

**Let us look at the next example on "Markup and markdown word problems answers"**

**Example 3 : **

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**

**Let us look at the next example on "Markup and markdown word problems answers"**

**Example 4 : **

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**

**Let us look at the next example on "Markup and markdown word problems answers"**

**Example 5 : **

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 %**

**Let us look at the next example on "Markup and markdown word problems answers"**

**Example 6 : **

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**

**Let us look at the next example on "Markup and markdown word problems answers"**

**Example 7 : **

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 the mark up rate?

**Solution :**

Cheated Value = 1000 - 800 = 200

False weight = 800

Mark up rate = (Cheated value/False weight)x100%

Mark up rate = (200/800)x100% = 25%**Hence, the mark up rate is 25 %**

**Let us look at the next example on "Markup and markdown word problems answers"**

**Example 8 :**

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 **

**Let us look at the next example on "Markup and markdown word problems answers"**

**Example 9 :**

Mr. Lenin sold a chair at a loss of 15%. If he had sold at a mark up rate 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**

**Let us look at the next example on "Markup and markdown word problems answers"**

**Example 10 :**

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

**Solution :**

As per the question, we need 15% mark up rate 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% mark up rate.**

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

That is,

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

Mark up rate = (270/1200) x 100

Mark up rate = 22.5 %

**Hence, the rest of the goods to be sold at the mark up rate of 22.5% in order to have the mark up rate of 15% overall.**

**Let us look at the next example on "Markup and markdown word problems answers"**

**Example 11 :**

By selling 20 articles, a trader gained the selling price of 5 articles. Find the mark up rate.

**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**

Mark up rate = (X / 3X).100% = (1/3).100%

Mark up rate = 33.33%

**Hence, the mark up rate is 33.33 %**

**Let us look at the next example on "Markup and markdown word problems answers"**

**Example 12 :**

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

Mark up rate = (160/360)x100 % = 44.44%

**Hence the mark up rate is 44.44 %**

**Let us look at the next example on "Markup and markdown word problems answers"**

**Example 13 :**

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

**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 ------> Mark up rate = 8 %

**Hence, the mark up rate is 8%**

**Let us look at the next example on "Markup and markdown word problems answers"**

**Example 14 :**

A person wants to get 20% mark up rate 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%**

**Let us look at the next example on "Markup and markdown word problems answers"**

**Example 15 :**

A person buys 8 articles for $15 and sells them at 10 for $18. Find the gain 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.**

**Let us look at the next example on "Markup and markdown word problems answers"**

**Example 16 :**

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%**

**Let us look at the next example on "Markup and markdown word problems answers"**

**Example 17 :**

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% 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.**

**Example 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%**

**Let us look at the next example on "Markup and markdown word problems answers"**

**Example 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%**

**Let us look at the next example on "Markup and markdown word problems answers"**

**Example 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.

Do you need the shortcuts explained above as pdf document?

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