**Problem 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)% ⋅ C.P

Here,

M = 40, C.P = $25

Then,

S.P = (100 + 40)% ⋅ 25

S.P = 140% ⋅ 25

S.P = 1.4 ⋅ 25

S.P = $35

So, the selling price is $35.

**Problem 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) ⋅ 100% = 87.5%

So, the mark up rate is 87.5 %

**Problem 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)% ⋅ C.P -----(1)

Here,

S.P = $63, m = 40

Substitute 63 for S.P and 40 for m in (1).

(1)-----> 63 = (100 + 40)% ⋅ C.P

63 = 140% ⋅ C.P

63 = 1.4 ⋅ C.P

63 / 1.4 = C.P

45 = C.P

So, the cost of a pair of shoes is $45.

**Problem 4 :**

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

**Solution : **

Selling price (S.P) = (100 - m)% ⋅ L.P -----(1)

Here,

L.P = $55, m = 25

Substitute 55 for L.P and 25 for m in (1).

(1)-----> S.P = (100 - 25)% ⋅ 55

S.P = 75% ⋅ 55

S.P = 0.75 ⋅ 55

S.P = 41.25

So, the selling price is $ 41.25.

**Problem 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) ⋅ 100%

Marked down rate = 25%

**Problem 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)% ⋅ Original price -----(1)

Here,

S.P = 127.46, m = 15

Substitute 127.46 for S.P and 15 for m in (1).

127.46 = (100 - 15)% ⋅ Original price

127.46 = 85% ⋅ Original price

127.46 = 0.85 ⋅ Original price

127.46 / 0.85 = Original price

149.95 = Original price

So, the original price is $ 149.95.

**Problem 7 :**

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 :**

Let x be the cost price of A.

Then, we have

Cost price of B = 1.15x

Cost price of C = 1.2(1.15x)

Cost price of C = 1.38x

**Given :** The cost of C is $1656.

1.38x = 1656

Divide each side by 1.38

x = 1200

So, the price at which A bought the item is $1200.

**Problem 8 :**

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 price of the chair?

**Solution :**

Let x be the cost price of the chair.

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

S.P (-15%) = 0.85x -----(1)

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

S.P (+10%) = 1.1x -----(2)

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

Then, we have

(2) - (1) = 100

1.1x - 0.85x = 100

0.25x = 100

25x = 10000

x = 400

So, the cost price of the chair is $400.

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