Question

How much percent above the cost price should a shopkeeper mark his goods so that after allowing a discount of 10% on the marked price, he gains 8%?

Answer 1

Hint: Assume the marked price of the item as Rs. 100, then according to the question we must find the cost at which the shopkeeper will sell it with a discount of 10% on it. It is given as a marked price – selling price and discount is calculated as $\dfrac{10}{100}\times 100=10$. Therefore, we will get the selling price = $\left( 100-10 \right)=Rs.90$. Similarly, we can find the cost price of that item. Cost price $=\dfrac{92}{100}\times 90$ as $\left( 100-8 \right)=92%$, which is the cost price of the item.

Complete step-by-step answer:
It is required in the question to find the price a shopkeeper has to mark on his product, before selling so that even after giving a discount of 10% on the marked price he earns a profit of 8% on it.
Let us assume the marked price of the item as Rs. 100. We are assuming marked price as Rs. 100 to make our calculations easy and we can directly relate Rs 100 with 100%.
As the shopkeeper has to give 10% discount while selling to the customer, the discount offered by the shopkeeper is $\dfrac{10}{100}\times 100=Rs.10$.
So, the shopkeeper will give the customer a discount of Rs 10 and sell the item at Rs 90 or the selling price of the item is Rs 90.
Let the shopkeeper earn a profit of Rs. x on selling that item and it should be equal to 8% as mentioned in the question. So, the profit of the shopkeeper is given as, $8%\text{ of }x=\left( \dfrac{8}{100}\times x \right)\Rightarrow Rs.\dfrac{8x}{100}$
According to this the selling price of the item will be,
$\dfrac{\left( 100+8 \right)x}{100}\Rightarrow Rs.\dfrac{108x}{100}$
We know that the shopkeeper has sold the item for Rs. 90, which is the selling price of the item.
On equating the selling prices, we get,
$\begin{align}
  & \dfrac{108x}{100}=90 \\
 & \Rightarrow x=\dfrac{90\times 100}{108} \\
 & \Rightarrow x=83.33 \\
\end{align}$
Therefore, we get the value of x = 83.33. We had assumed x as the cost price of the item, so the cost price of the item = Rs. 83.33.
Thus, if the cost price of the item is Rs. 83.33 and if the shopkeeper wants to sell it at a profit of 8% along with a discount of 10% to the customer, then let the marked price of the item be Rs. 100. So,the marked price above the cost price would be Rs. (100 – 83.33) = Rs. 16.67.
The percentage of the marked price above cost price would be,
$\dfrac{16.67}{83.33}\times 100\Rightarrow 20%$
So, the conclusion is that the shopkeeper must increase the cost price of the item by 20% to give a discount of 10% to the customer and make a profit of 8% for himself at the same time.

Note: If the initial cost of the item is Rs. 83.33, then to make a profit of 8%, the shopkeeper has to sell that item at,
$\begin{align}
  & \left( CP+\dfrac{8}{100}\times 83.34 \right) \\
 & \Rightarrow 83.34+0.08\times 83.34 \\
 & \Rightarrow Rs.90 \\
\end{align}$
So, the shopkeeper has to sell the item at Rs. 90 and again if he wants to give a 10% discount to the customer, he has to increase the selling price by 10%. So, we get the marked price as,
$90+\dfrac{10}{100}\Rightarrow 90+10\Rightarrow Rs.100$
Therefore, we get the marked price of the item as Rs. 100, selling price of the item after 10% discount is Rs. 90 and the cost price with an 8% profit is Rs. 83.34.