# Profit Loss Involving Tax

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 mark-up 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, mark-up 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%

● Sales Tax and Value Added Tax