The marked

The marked price of the item was P62.50. At a seasonal sale, a discount was given 20% discount, leaving the dealer a profit of 14 2/7 % of the cost of each item. Find the profit and the cost price.

Correct answer:

p =  7 ¹⁄₇ = 50/7 P
c =  42 ⁶⁄₇ = 300/7 P

Step-by-step explanation:

$$\begin{gathered} a=62.50 \\ d=20\%=\frac{20}{100}=\frac{1}{5}=0.2 \\ R=14\frac{2}{7}=14+\frac{2}{7}=\frac{14\cdot 7+2}{7}=\frac{98+2}{7}=\frac{100}{7}\doteq 14.2857\% \\ r=R/100=\frac{100}{7}/100=\frac{100}{7\cdot 100}=\frac{100}{700}=\frac{1}{7}\doteq 0.1429 \\ b=a-d\cdot a=62.5-0.2\cdot 62.5=50\text{P} \\ p=r\cdot b=\frac{1}{7}\cdot 50=\frac{1\cdot 50}{7}=\frac{50}{7}=\frac{50}{7}\text{P}=7\frac{1}{7}\text{P}=7.1429\text{P} \end{gathered}$$

$c=b-p=50-\frac{50}{7}=\frac{50\cdot 7}{7}-\frac{50}{7}=\frac{350}{7}-\frac{50}{7}=\frac{350-50}{7}=\frac{300}{7}=\frac{300}{7}\text{P}=42.8571\text{P}$

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