**Cost price = [100 / (100 - loss%)] ⋅ Selling price**

**Cost price = [100 / (100 + profit%)] ⋅ Selling price**

**Example 1 :**

A bag was sold for $324 there by loss 8%. Find the cost price of the bag.

**Solution :**

Selling price of the bag = $324

This selling price includes 8% loss. To find the cost price, we use the formula

Cost price = [100 / (100 - loss%)] ⋅ Selling price

Cost price = [100/(100 - 8)] ⋅ 324

= (100/92) ⋅ 324

= $352.17

Hence the cost price of the bag is $352.17

**Example 2 :**

A trademan sold an article at a loss of 20%. If the selling price had been increased by $100, there would have been gain of 5%. What was the cost price of the article ?

**Solution :**

Let x be the cost price of an article.

Cost price when loss happened = 80% of x

= 80x/100

= 4x/5

Cost price when profit happened = 105% of x

= 105x/100

= 21x/20

The difference between two cost prices = 100

(21x/20) - (4x/5) = 100

(21x-16x)/20 = 100

5x = 100(20)

x = 400

Hence the required cost price is 400.

**Example 3 :**

A man sells an article at a profit of 25%. If he had bought it at 20% less and sold it for $1050 less, he would have gained 30%. How do I find the cost price of the article?

**Solution :**

Let x be the cost price of the article.

After 25% profit made, the selling price will be 125% of x.

Selling price = 125x/100

Profit earned is 30% when the selling price be 1050 lesser than the previous price.

New selling price of the article = 125x/100 - 1050

If cost price of article 20% less, then cost price = 80% of x

Profit% = (Selling price - Cost price)/Cost price

30% = {[1.25x - 1050] - 0.80x}/0.8x

30(0.8x) = (1.25x - 1050 - 0.80x)

0.24x = 0.45x - 1050

1050 = 0.45x - 0.24x

0.21x = 1050

x = 1050/0.21

x = 5000

Hence the cost price of the article is $5000.

**Example 4 :**

A man sells an article at a profit of 25%. If he had bought it at 20% less and sold it for rupees 36.75 an less he would have gained 30%. Find the cost price of article.

**Solution :**

Let x be the cost price of the article.

After 25% profit made, the selling price will be 125% of x.

Selling price = 125x/100

Profit earned is 30% when the selling price be 1050 lesser than the previous price.

New selling price of the article = 125x/100 - 36.75

If cost price of article 20% less, then cost price = 80% of x

Profit% = (Selling price - Cost price)/Cost price

30% = {[1.25x - 36.75] - 0.80x}/0.8x

0.3(0.8x) = (1.25x - 36.75 - 0.80x)

0.24x = 0.45x - 36.75

36.75 = 0.45x - 0.24x

0.21x = 36.75

x = 36.75/0.21

x = 175

Hence the cost price of the article is $175.

Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here

If you have any feedback about our math content, please mail us :

**v4formath@gmail.com**

We always appreciate your feedback.

You can also visit the following web pages on different stuff in math.

**WORD PROBLEMS**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Trigonometry word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**