Profit and loss

Find the cost price and the profit and loss if the percent of profit and loss is based on cost price, Selling Price P2.34, and the percent of profit is 8 1/3%. Find the profit and cost price.

Correct answer:

p =  9/50
x =  2 ⁴⁄₂₅ = 54/25

Step-by-step explanation:

$$\begin{gathered} m=8\frac{1}{3}=8+\frac{1}{3}=\frac{8\cdot 3+1}{3}=\frac{24+1}{3}=\frac{25}{3}=8\frac{1}{3}\doteq 8.3333 \\ r=m/100=\frac{25}{3}/100=\frac{25}{3\cdot 100}=\frac{25}{300}=\frac{1}{12}\doteq 0.0833 \\ 2.34=r\cdot x+x \\ x=2.34/(1+r)=2.34/(1+\frac{1}{12})=\frac{54}{25}=2\frac{4}{25}=2.16 \\ p=r\cdot x=\frac{1}{12}\cdot \frac{54}{25}=\frac{1\cdot 54}{12\cdot 25}=\frac{54}{300}=\frac{9}{50}=0.18 \end{gathered}$$

$x=\frac{54}{25}=2\frac{4}{25}=2.16$

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