Cost Price and Selling Price Aptitude Formulas, Definitions, & Examples:

Overview:

Selling Price Formula:

$$ SP = \frac{100 \pm Profit/Loss \ \%}{100} \times CP $$

Cost Price Formula:

$$ CP = \frac{SP \times 100}{100 \pm Profit/Loss \ \%} $$

In the formulas given above, if out of three unknown, two are given in the question then you can simply find out the third unknown.

Note: use positive (+) sign if in the question the value of profit % is given or asks to find profit % and use negative (-) sign if in the question the value of loss % is given or asks to find loss %.

Example (1): A seller named Ram sold a book for \(Rs.200\) and made a profit of \(10 \ \%\). What will be the Cost Price (CP) of the book?

Solution: Given values are Selling Price \((SP) = Rs.200\), \(Profit \ \% = 10 \ \%\).

According to case (1)- $$ SP = \frac{100 \pm Profit/Loss \ \%}{100} \times CP $$ $$ 200 = \frac{100 + 10}{100} \times CP $$ $$ 200 = \frac{110}{100} \times CP $$ $$ Cost \ Price \ (CP) = \frac{20000}{110} $$ $$ = 181.81 \ (Answer) $$

Example (2): A seller sold an article with the loss of \(10 \ \%\) for \(Rs.300\). What will be the Cost Price (CP) of the article?

Solution: Given values are Selling Price \((SP) = Rs.300\), \(loss \ \% = 10 \ \%\).

According to case (1)- $$ SP = \frac{100 \pm Profit/Loss \ \%}{100} \times CP $$ $$ 300 = \frac{100 - 10}{100} \times CP $$ $$ 300 = \frac{90}{100} \times CP $$ $$ Cost \ Price \ (CP) = \frac{30000}{90} $$ $$ = 333.33 \ (Answer) $$

Example (3): A man purchased an article for \(Rs.500\) and sold with the loss of \(20 \ \%\). What will be the selling Price (SP) of the article?

Solution: Given values are Cost Price \((CP) = Rs.500\), \(loss \ \% = 20 \ \%\).

According to case (1)- $$ SP = \frac{100 \pm Profit/Loss \ \%}{100} \times CP $$ $$ SP = \frac{100 - 20}{100} \times 500 $$ $$ SP = \frac{80}{100} \times 500 $$ $$ SP = 400 \ (Answer) $$