Question

a shirt is marked at a price to earn 30% of profit after giving a discount of 20%.What is the percentage by which the shirt is marked over the original price

Answer 1

50 percent by the shirt is marked over the original price

Answer 2

The percentage by which the shirt is marked over the original price is 62.5%.

Step-by-step explanation:

Let the marked price is Rs. x and the original price is assumed to be y Rs.

So, the percentage by which the shirt is marked over the original price is

$\frac{x - y}{y} \times 100\% = (\frac{x}{y} - 1) \times 100\%$

Now, giving a discount of 20% on the marked price makes the selling price $x(1 - \frac{20}{100}) = 0.8x$.

Now, this selling price will give a 30% profit on the original price.

So, $\frac{0.8x - y}{y} = \frac{30}{100} = 0.3$

⇒ 0.8x - y = 0.3y

⇒ 0.8x = 1.3y

⇒ $\frac{x}{y} = \frac{1.3}{0.8} = 1.625$

⇒ $\frac{x}{y} - 1 = 1.625 - 1 = 0.625$

⇒ $(\frac{x}{y} - 1) \times 100 = 0.625 \times 100 = 62.5\%$

Therefore, the percentage by which the shirt is marked over the original price is 62.5%. (Answer)