Question

Selling price without tax of a pair of sports shoes is $83⅓\%$ of its final price with tax. Find the tax percentage.

• A. $5\%$
• B. $13\%$
• C. $20\%$
• D. $10\%$

Answer 1

The correct option is C $20\%$

Let the selling price be $“a”$.
Let the billing price (SP + tax) be $“b”$.
Let the tax percentage be $“x”$ .
From the condition we have,
selling price without tax is $83\frac{1}{3}\%$ of its selling price after tax.
$a=\frac{83\frac{1}{3}\%}{100}\times b$

$\frac{b}{a}=\frac{100}{83\frac{1}{3}}$

Tax amount $=b-a$

Tax percentage $=\frac{(b-a)}{a}\times 100$

$x=(\frac{b}{a}-1)\times 100$

$x=(\frac{100}{83\frac{1}{3}}-1)\times 100$
$x=(\frac{100}{\frac{250}{3}}-1)\times 100$
$x=(\frac{300}{250}-1)\times 100$

$x=\frac{50}{250}\times 100$

$x=20\%$