We will discuss here how to solve the problems based on Profit loss involving tax.
1. A shopkeeper buys a DVD player at a rebate of 20% on the printed price. He spends $ 20 on transportation of the DVD player. After changing a sales tax 6% on the printed price, he sells the DVD player at $530. Find his profit percentage.
Solution:
Let the printed price be P. Then, the cost price = P – 20% of P = P – \(\frac{20P}{100}\) = \(\frac{4P}{5}\).
Actual cost price including transportation cost = \(\frac{4P}{5}\) + $ 20.
The sales tax = 6% of P = \(\frac{6P}{100}\) = \(\frac{3P}{50}\)
Therefore, the selling price including sales tax = P + \(\frac{3p}{50}\)
According to the problem,
P + \(\frac{3P}{50}\) = \(\frac{53P}{50}\) = $ 530
\(\frac{53P}{50}\) = $ 530
Therefore, P = $ 500
Therefore, the actual cost price = \(\frac{4P}{5}\) + $ 20 = \(\frac{4 × $ 500}{5}\) + $ 20 = $ 420.
Therefore, profit = printed price – actual cost price = $ 500  $ 420 = $ 80.
Therefore, profit percentage = \(\frac{$ 80}{$ 420}\) × 100% = \(\frac{400}{21}\)% = 19\(\frac{1}{21}\) %.
2. A seller buys a LED Televisions for $ 2500 and marks up its price. A customer buys the LED Televisions for $ 3,300 which includes a sales tax of 10% on the marked up price.
(i) Find the markup percentage on the price of the LED Televisions.
(ii) Find his profit percentage.
Solution:
Let the marked up price be P. Then, the sales tax = 10% of P = P/10.
Therefore, selling price = P + \(\frac{P}{10}\)
According to the problem, = $ 3300
Or, P ∙ \(\frac{11}{10}\) = $ 3300
Therefore, P = $ 3000.
Therefore, $ 2500 is marked up to $ 3000
Therefore, markup percentage = \(\frac{$ 300  $ 2500}{2500}\) × 100% = \(\frac{500}{2500}\) × 100% = 20%
Now, the profit = marked up price – cost price = $ 3000  $ 2500 = $ 500
Therefore, profit percentage = \(\frac{$ 500}{$ 2500}\) × 100% = 20%
Markups and Discounts Involving Sales Tax10th Grade Math
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