Cost price (CP) is the price at which an article is purchased.
Selling price (SP) is the price at which an article is sold.
If SP > CP, it is a profit or gain
If CP > SP, it is a loss.
Gain or Profit = SP – CP
Loss = CP - SP
Loss or gain is always reckoned on CP
Profit Percentage (Profit %) = $MF#%\dfrac{\text{Profit}}{\text{CP}}\times 100 = \dfrac{\left(\text{SP - CP}\right)}{\text{CP}}\times 100$MF#%
Loss Percentage (Loss %) = $MF#%\dfrac{\text{Loss}}{\text{CP}}\times 100 = \dfrac{\left(\text{CP - SP}\right)}{\text{CP}}\times 100$MF#%
In the case of a gain or profit,
$MF#%\text{SP} = \dfrac{\left(100 + \text{Gain} \% \right)} {100}\times \text{CP} $MF#%
$MF#%CP = \dfrac{100} {\left(100 +\text{ Gain }\% \right)}\times \text{SP} $MF#%
In the case of a loss,
$MF#%SP = \dfrac{\left(100 - \text{Loss} \%\right) } {100}\times \text{CP} $MF#%
$MF#%CP = \dfrac{100} {\left(100 - \text{Loss} \% \right)}\times \text{SP} $MF#%
If an article is sold at a gain of 20%, then SP = 120% of CP
If an article is sold at a loss of 20% then SP = 80% of CP
If an article is sold at a loss of 20% then SP = 80% of CP
If a person sells two items at the same price; one at a gain of x % and another at a loss of x %, then the seller always incurs a loss expressed as
$MF#%\text{Loss }\% = \left(\dfrac{\text{ Common Loss and Gain }\% } {10}\right)^2 = \left(\dfrac{ x } {10}\right)^2$MF#%
If a trader professes to sell his goods at cost price, but uses false weights, then
$MF#%Gain \% = \left[\dfrac{ \text{Error}} {\left(\text{ True Value - Error }\right)} \times 100 \right] \% $MF#%
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