Question

A shopkeeper offers a 10% discount on all his items. During the festival season, he decided to give a further discount of 20% over and above the existing discount. Find the actual selling price of the following items.
(i) a set of frying pans of marked price Rs. 1000.
(ii) A suit of marked price Rs. 2500
(iii) An electric iron of marked price Rs. 1250
(iv) A table cloth of marked price Rs. 375

Answer 1

Hint: First, we will let the general marked price as Rs. x. Then, we will get the overall discounted price for each item after successive discounts of 10% and 20% is $\dfrac{72x}{100}$. Then, on getting the overall discount, we will find the discounted price of each item given in the question.

Complete step-by-step answer:
In this question, we are supposed to find the successive discount of 10% and then 20% on the marked price of various items.
So, let us consider the general marked price as Rs. x.
Then, by applying the first discount of 10% over marked price Rs. x is given by:
$\begin{align}
  & x-\dfrac{10x}{100}=\dfrac{100x-10x}{100} \\
 & \Rightarrow \dfrac{90x}{100} \\
\end{align}$
So, the first discounted price is $\dfrac{90x}{100}$ which is further discounted by 20% given by:
$\begin{align}
  & \dfrac{90x}{100}-\dfrac{20}{100}\times \dfrac{90x}{100}=\dfrac{90x}{100}-\dfrac{18x}{100} \\
 & \Rightarrow \dfrac{72x}{100} \\
\end{align}$
So, the overall discounted price for each item after successive discounts of 10% and 20% is $\dfrac{72x}{100}$.
(1) Now, for solving it for the case of a set of frying pans of marked price Rs. 1000.
Here, the value of x is 1000, so the discounted price is:
$\dfrac{72}{100}\times 1000=720$
So, the actual selling price of the frying pans is RS. 720.
(ii) Similarly, for solving it for the case of a suit of marked price Rs. 2500
Here, the value of x is 2500, so the discounted price is:
$\dfrac{72}{100}\times 2500=1800$
So, the actual selling price of the case of suit is RS. 1800.
(iii)Similarly, for solving it for an electric iron of marked price Rs. 1250
Here, the value of x is 1250, so the discounted price is:
$\dfrac{72}{100}\times 1250=900$
So, the actual selling price of an electric iron is RS. 900.
(iv) Similarly, for solving it for a table cloth of marked price Rs. 375
Here, the value of x is 375, so the discounted price is:
$\dfrac{72}{100}\times 375=270$
So, the actual selling price of a tablecloth is RS. 270.

Note: In this type of question the only mistake we can do is that we can take the successive discounts of 10% and 20% as total of 30% which is a wrong assumption and will lead to the discounted price as
 $\begin{align}
  & x-\dfrac{30x}{100}=\dfrac{100x-30x}{100} \\
 & \Rightarrow \dfrac{70x}{100} \\
\end{align}$
Which is a wrong value of discounted as the second discount is given on the first discounted value which leads to an overall discount of $\dfrac{72x}{100}$.