Question

at what profit percent must an article be sold so that by selling at half price,there may be a loss of 30%​

Answer 1

The profit percent obtained is 40%.

• We need to calculate the profit percent of the article when the selling price is reduced to half , it incurs a loss of 30%.
• Now we assume the selling price of the article as x, and the cost price be y.
• Now to calculate profit = Selling price -Cost price = x - y
• Now to calculate loss = Cost price - Selling price = y - x
• Now when selling price is reduced to half, loss is 30%.

Loss percentage = $\frac{Loss}{Cost \ price}$ × 100

• Now, loss = Cost price  - selling price = y - x/2

• Loss percentage = $\frac{y-x/2}{y}$ × 100 = 30

y-x/2 = 0.3y

2y - x = 0.6y

x = 1.4y   (Equation 1)

• We have to calculate the profit percentage,

Profit percentage = $\frac{Profit}{Cost \ price}$ × 100

Profit percentage = $\frac{x-y}{y}$ × 100

• Substituting the value of x in the above equation from equation 1

Profit percentage = $\frac{1.4y-y}{y}$ × 100

Profit percentage = $\frac{0.4y}{y}$ × 100 = 0.4 × 100 = 40%.