**Word Problems on Percentage 5 : **

This is the continuity of our web content given on "Word problems on Percentage".

Before we look at the problems, if you want to know the shortcuts required for solving percentage problems,

**Problem 1 : **

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 %

**Problem 2 : **

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

Plugging the above values in (1), we get

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

Hence, the original price is $ 149.95

**Problem 3 :**

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 ) ⋅ 100 %

= (5m / 20m) ⋅ 100 %

= 25%

Hence, the mark up rate is 25%

**Problem 4 :**

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 ⋅ profit = 5 ⋅ 20 = $100

Cost price = Selling price - Profit

Cost price = 100 - 20 = $80

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

= (20 / 80) ⋅ 100 %

= 25%

Hence, the mark up rate is 25%

**Problem 5 :**

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.

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