FIND COST PRICE WHEN SELLING PRICE AND LOSS PERCENT IS GIVEN

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

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

Examples

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.

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