Question

If a man incurs a loss of 20 percent by selling an article for Rupees 1000. At what price should he sell it to make a profit of 16 percent.

Answer 1

Hint: we are given loss percentage and selling price we can easily find out the cost price of the product with help of two formulas loss percentage is $\dfrac{\text{loss}}{\text{CP}}\times 100$ and loss is Cost price – selling price

Complete step-by-step answer:
Now we are given that a man incurs a loss of 20 percent by selling an article for Rupees 1000.
Hence we have Selling price (SP) = 1000 and Loss percentage = 20.
Let x be the Cost price (CP) of the product.
We know that loss = Cost price - Selling price.
Hence Loss = x – 100
Now Loss percentage is nothing but $\dfrac{\text{loss}}{\text{CP}}\times 100$
Hence now we have $20=\dfrac{x-1000}{x}\times 100$
Now dividing throughout by 20 to simplify the equation we get
$1=\dfrac{5(x-1000)}{x}$
Now let us multiply the equation with x
$\begin{align}
  & x=5(x-1000) \\
 & \Rightarrow x=5x-5000 \\
 & \Rightarrow 6x=5000 \\
 & \Rightarrow x=\dfrac{5000}{6} \\
\end{align}$
$x=\dfrac{5000}{6}$
Hence CP is $\dfrac{5000}{6}...............(1)$
Now, we want to make a profit of 16 percent. Let y be SP such that we make a profit of 16 percent.
So we have Profit = selling price – cost price
Hence from equation (1) we get
Profit = $y-\dfrac{5000}{6}$
Now profit percentage is calculated with formula $\dfrac{\text{profit}}{\text{CP}}\times 100$
$20=\dfrac{y-\dfrac{5000}{6}}{\dfrac{5000}{6}}$
Simplifying the equation
 $\begin{align}
  & 20\times \dfrac{5000}{6}=y-\dfrac{5000}{6} \\
 & \Rightarrow \dfrac{10000}{6}=y-\dfrac{5000}{6} \\
 & \Rightarrow \dfrac{10000}{6}+\dfrac{5000}{6}=y \\
 & \Rightarrow y=\dfrac{15000}{6}=2500 \\
\end{align}$
Hence we have value of y is 2500 Rupees and hence Selling price is 2500 Rupees
Hence to make a profit of 20 percent we should sell the product at 2500 Rupees.

Note: While Calculating profit we take selling price – cost price since selling price is more than cost price for a profit. Similarly while calculating loss we take cost price – selling price since cost price is more than selling price in loss.