Answer

Verified

447.6k+ views

**Hint**: We know that if p is the single discount of discount series of \[{{x}_{1}},{{x}_{2}},......,{{x}_{n}}\]., then \[p=\left( 1-\prod\limits_{i=1}^{n}{\left( \dfrac{100-{{x}_{i}}}{100} \right)} \right)\times 100\]. From the question, it is given to find the single discount of the discount series of \[10\%\] and \[20\%\]. By using the above formula, we can find the single discount of the discount series of \[10\%\] and \[20\%\].

**:**

__Complete step-by-step answer__Before solving the question, we should know that if p is the single discount of discount series of \[{{x}_{1}},{{x}_{2}},......,{{x}_{n}}\]., then \[p=\left( 1-\prod\limits_{i=1}^{n}{\left( \dfrac{100-{{x}_{i}}}{100} \right)} \right)\times 100\].

Now by using this formula, we can find the single discount of a certain discount series.

From the question, it is clear that we have to find the discount series of \[10\%\] and \[20\%\].

We know that if p is the single discount of discount series of \[{{x}_{1}},{{x}_{2}},......,{{x}_{n}}\]., then\[p=\left( 1-\prod\limits_{i=1}^{n}{\left( \dfrac{100-{{x}_{i}}}{100} \right)} \right)\times 100\].

So, we get

\[\begin{align}

& \Rightarrow p=\left( 1-\left( \dfrac{100-10}{100} \right)\left( \dfrac{100-20}{100} \right) \right)\times 100 \\

& \Rightarrow p=\left( 1-\left( \dfrac{90}{100} \right)\left( \dfrac{80}{100} \right) \right)\times 100 \\

& \Rightarrow p=\left( 1-\dfrac{72}{100} \right)\times 100 \\

& \Rightarrow p=\left( \dfrac{100-72}{100} \right)\times 100 \\

& \Rightarrow p=\left( \dfrac{28}{100} \right)\times 100 \\

& \Rightarrow p=28.....(1) \\

\end{align}\]

From equation (1), it is clear that the value of p is equal to 28. So, we can say that a single discount is equal to the discount series of \[10\%\] and \[20\%\] is \[28\%\].

**So, the correct answer is “Option D”.**

**Note**: Students may have a misconception that if p is the single discount of discount series of \[{{x}_{1}},{{x}_{2}},......,{{x}_{n}}\]., then \[p=\left( \prod\limits_{i=1}^{n}{\left( \dfrac{100-{{x}_{i}}}{100} \right)} \right)\times 100\]. If this misconception is followed, then we get

\[\begin{align}

& \Rightarrow p=\left( \left( \dfrac{100-10}{100} \right)\left( \dfrac{100-20}{100} \right) \right)\times 100 \\

& \Rightarrow p=\left( \left( \dfrac{90}{100} \right)\left( \dfrac{80}{100} \right) \right)\times 100 \\

& \Rightarrow p=\left( \dfrac{72}{100} \right)\times 100 \\

& \Rightarrow p=72.....(1) \\

\end{align}\]

From equation (1), it is clear that the value of p is equal to 28. So, we can say that a single discount is equal to the discount series of \[10\%\] and \[20\%\] is \[72\%\]. But we know that the single discount is equal to \[28\%\]. So, this misconception should get avoided.

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Mark and label the given geoinformation on the outline class 11 social science CBSE

When people say No pun intended what does that mea class 8 english CBSE

Name the states which share their boundary with Indias class 9 social science CBSE

Give an account of the Northern Plains of India class 9 social science CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Trending doubts

Difference Between Plant Cell and Animal Cell

Which are the Top 10 Largest Countries of the World?

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

How do you graph the function fx 4x class 9 maths CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths