Question

the cost price of 30 eggs is equal to the sale price of 20 eggs. what is the percentage of profit?​

Answer 1

The cost price of 30 eggs is equal to the sale price of 20 eggs. The profit percentage is 50 %

S O L U T I O N :

$\sf Let \:the \:cost \:price \:of \:1 \:egg \:be\: x$

$\sf Then \:the\: cost \:price\: of\: 30 \:eggs = 30x$

$\sf Let \:the \:selling \:price\: of \:one\: egg = y$

$\sf Then\: the\: selling \:price \:of\: 20 eggs = 20y$

$\sf Selling\: price\: of \:30 \:eggs = 30y$

Given that,

Cost price of 30 eggs is equal to the sale price of 20 eggs 30x = 20y

$\begin{gathered}3x = 2y\\\\y = \frac{3x}{2} ------ eqn 1\end{gathered}$

Profit = Selling price - cost price

Profit = 30y - 30x

• From eqn 1,

$\begin{gathered}\sf profit = 30(\frac{3x}{2}) -30x\\\\\sf profit = 45x - 30x\\\\profit = 15x\end{gathered}$

The profit percentage is given as:

$\begin{gathered}\sf Profit\ percentage = \frac{profit}{cost\ price} \times 100\\\\\sf Profit\ percentage = \frac{15x}{30x} \times 100\\\\ Profit\ percentage = 0.5 \times 100\\\\Profit\percentage = 50 \%\end{gathered}$

Thus profit percentage is 50 %

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