The original price $P$ of a certain item is first discounted by $20$ percent and then $5$ percent of the discount price is added for sales tax. If the final price, including the sales tax is $$ 71.40$ , calculate the original price $P$ .

$ 59.50

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$ 81.40

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$ 84.00

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$ 85.00

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$ 86.40

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Solution

The correct option is B $$ 85.00$
Given, $P$ is the original price of item and get $20 %$ discount.
Then discounted price $=$ $\frac{80}{100} P = \frac{4}{5} P$
Then sale tax $5 %$ on discounted price $=$ $\frac{5}{100} \times \frac{4}{5} P = \frac{1}{25} P$ .
Then total cost $=$ $\frac{4}{5} P + \frac{1}{25} P$
But total cost is $71.40$ ....... (given)
Therefore, $\frac{4}{5} P + \frac{1}{25} P = 71.40$
$\Rightarrow 20 P + P = 1785$
$\Rightarrow 21 P = 1785$
$\Rightarrow P = 85$

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The original price P of a certain item is first discounted by 20 percent and then 5 percent of the discount price is added for sales tax. If the final price, including the sales tax is $71.40, calculate the original price P.

The original price $P$ of a certain item is first discounted by $20$ percent and then $5$ percent of the discount price is added for sales tax. If the final price, including the sales tax is $$ 71.40$ , calculate the original price $P$ .