All Profit and Loss Formulas in One Place

Rumman Ansari   Software Engineer   2023-03-30   113 Share
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Table of Content:

All Profit and Loss Formulas in One Place

\begin{align} Profit = Selling\: price \: – cost \: price \end{align}
\begin{align} Loss = cost \:price \: – selling \: price \end{align}
\begin{align} Profit \%= \frac{profit}{cost \: price} \times 100 \end{align}
\begin{align} Loss \%= \frac{loss}{cost \: price} \times 100 \end{align}
\begin{align} Selling \:price \: = \left[ 1 + \frac{ gain \%}{100}\ \right] \times cost \:price \end{align}
\begin{align} Selling \:price \: = \left[ 1 + \frac{ loss \%}{100}\ \right] \times cost \:price \end{align}

Example

Find the profit%, if an article worth Rs.300 is sold for Rs. 312?

\begin{align} Profit &= Selling\: price \: – cost \: price \\ &= 312 – 300 \\ &= 12 \end{align} \begin{align} Profit \% &= \frac{profit}{cost \: price} \times 100 \\ &= \frac{12}{300} \times 100 \\ &= 4\% \end{align}

Percentage reduction in consumption:

If the rate of a commodity is increased, then the consumption should be reduced to maintain the same expenditure.

\begin{align} Percentage \:reduction\: in\: consumption \: &= \\ &= \frac{ \% \:change}{100 + \: \% \:change} \times 100 \\ &= \frac{ 25}{100 + 25} \times 100 \\ &= 20 \% \end{align}

So the Quantity of rice consumption should be reduced by 20% to maintain same expenditure.

Successive Discount:

If two successive discounts of a% and b% are offered then the net discount offered is

\begin{align} \left[ a + b - \frac{a \times b}{100}\ \right] \% \end{align}

Example

Find the net discount offered on two successive discounts of 20% and 30%?

\begin{align} Net Discount &= \left[a + b - \frac{a \times b}{100}\ \right] \% \\ &= \left[20 + 30 - \frac{20 \times 30}{100}\ \right] \% \\ &= 44 \% \end{align}

Discount is the reduction of price. If a% discount is offered then the article would be sold for (100 – a) % of marked price

\begin{align} Selling \:price \: = \left[ 1 + \frac{ 100 - a}{100}\ \right] \times market \:price \end{align}

False Weight:

In case a false weight which is less than the actual weight is used then the transaction ends in a profit

\begin{align} \% \:Profit = \left[ \frac{ Error}{True \: value - \: Error }\ \times 100 \right] \end{align}

Example

If a shop keeper sells 800gms at cost price claiming it to be 1kg, find the gain%?

\begin{align} \% \:Profit &= \left[ \frac{ Error}{True \: value - \: Error }\ \times 100 \right] \\ &= \left[ \frac{ 200}{1000 - \: 200}\ \times 100 \right] \\ &= 25 \% \end{align}

In case where selling price of two articles is the same and one is sold at a loss of x%, and other at a profit of x% then this transaction always leads to a loss of

\begin{align} \frac{ x^2}{ 100 } \% \end{align}
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