Question

Match the following with their respective formula.

• A. $S.P.-C.P.$
• B. $C.P.-S.P.$
• C. $\frac{Profit}{C.P.}\times 100$
• D. $\frac{Profit\%+100}{100}\times C.P.$

Answer 1

The price, at which an article is purchased, is called its cost price, abbreviated as C.P.

The price, at which an article is sold, is called its selling price, abbreviated as S.P.

If S.P. is greater than C.P., the seller is said to have a profit or gain.

$\therefore$ Profit = S.P - C.P

If S.P. is less than C.P., the seller is said to have incurred a loss.

$\therefore$ Loss = C.P - S.P

Profit % is given by $\frac{\text{profit}}{\text{C.P}}\times 100$.

$\because$ Profit = S.P - C.P
$\Rightarrow$ Profit % = $\frac{\text{S.P - C.P}}{\text{C.P}}\times 100$
= $[\frac{\text{S.P}}{\text{C.P}}-1]\times 100$
$\Rightarrow$ $\frac{\text{S.P}}{\text{C.P}}\times 100$ = profit % + 100
$\Rightarrow \text{S.P}=\frac{\text{profit}\%+100}{100}\times \text{C.P}$