Answer
Verified
376.5k+ views
Hint: To find the value of 20% of 50% of 75% of 80, firstly, we have to find the value 75% of 80. For this, we have to convert 75% into its number form by dividing 75 by 100. Then, we have to find 50% of 75% of 80, that is, 50% of the result of 75% of 80. Finally, we have to find the value of 20% of this result.
Complete step by step solution:
We have to find the value of 20% of 50% of 75% of 80. First let us find the value of 75% of 80. We can write this mathematically as
$\Rightarrow 75\%\times 80$
We know that to convert a percentage into a number, we have to divide that percentage by 100. Therefore, 75% can be written as $\dfrac{75}{100}$ . Hence, the above expression becomes
$\Rightarrow 75\%\times 80=\dfrac{75}{100}\times 80$
Let us cancel the zeroes from the numerator and the denominator.
\[\Rightarrow 75\%\times 80=\dfrac{75}{10\require{cancel}\cancel{0}}\times 8\require{cancel}\cancel{0}\]
We can write the result of the above simplification as
\[\Rightarrow 75\%\times 80=\dfrac{75}{10}\times 8\]
Let us cancel the common factor 5.
\[\begin{align}
& \Rightarrow 75\%\times 80=\dfrac{{{\require{cancel}\cancel{75}}^{15}}}{{{\require{cancel}\cancel{10}}^{2}}}\times 8 \\
& \Rightarrow 75\%\times 80=\dfrac{15}{2}\times 8 \\
\end{align}\]
We can cancel the common factor 2.
\[\begin{align}
& \Rightarrow 75\%\times 80=\dfrac{15}{\require{cancel}\cancel{2}}\times {{\require{cancel}\cancel{8}}^{4}} \\
& \Rightarrow 75\%\times 80=15\times 4 \\
& \Rightarrow 75\%\times 80=60 \\
\end{align}\]
Therefore, 75% of 80 is 60.
Now, we have to find 50% of 75% of 80, that is, 50% of 60. We can write this mathematically as
$\Rightarrow 50\%\times 60$
We have to convert 50% into its number form.
$\Rightarrow 50\%\times 60=\dfrac{50}{100}\times 60$
Let us simplify the above expression by cancelling the zeroes from the numerator and the denominator.
$\begin{align}
& \Rightarrow 50\%\times 60=\dfrac{5\require{cancel}\cancel{0}}{1\require{cancel}\cancel{0}\require{cancel}\cancel{0}}\times 6\require{cancel}\cancel{0} \\
& \Rightarrow 50\%\times 60=5\times 6 \\
& \Rightarrow 50\%\times 60=30 \\
\end{align}$
Therefore, 50% of 60 is 30.
Now, let us find 20% of 50% of 75% of 80, that is, 20% of 50% of 60, or 20% of 30. We have to write the mathematical form of 20% of 30.
$\Rightarrow 20\%\times 30$
We have to convert 20% into its number form.
$\Rightarrow 20\%\times 30=\dfrac{20}{100}\times 30$
Let us simplify the above expression by cancelling the zeroes from the numerator and the denominator.
$\begin{align}
& \Rightarrow 20\%\times 30=\dfrac{2\require{cancel}\cancel{0}}{1\require{cancel}\cancel{0}\require{cancel}\cancel{0}}\times 3\require{cancel}\cancel{0} \\
& \Rightarrow 20\%\times 30=2\times 3 \\
& \Rightarrow 20\%\times 30=6 \\
\end{align}$
Therefore, 20% of 50% of 75% of 80 is $6$. So, the correct answer is “Option (b)”.
Note: Students have a chance of making a mistake by first finding 20% of 50%, then finding the result of this of 75%, and so on, that is, doing the forward operation. In these types of questions, we have to find the answer backwards. Students must learn to convert a number into its percentage and vise-versa. We can do the former operation by multiplying the number by 100.
Complete step by step solution:
We have to find the value of 20% of 50% of 75% of 80. First let us find the value of 75% of 80. We can write this mathematically as
$\Rightarrow 75\%\times 80$
We know that to convert a percentage into a number, we have to divide that percentage by 100. Therefore, 75% can be written as $\dfrac{75}{100}$ . Hence, the above expression becomes
$\Rightarrow 75\%\times 80=\dfrac{75}{100}\times 80$
Let us cancel the zeroes from the numerator and the denominator.
\[\Rightarrow 75\%\times 80=\dfrac{75}{10\require{cancel}\cancel{0}}\times 8\require{cancel}\cancel{0}\]
We can write the result of the above simplification as
\[\Rightarrow 75\%\times 80=\dfrac{75}{10}\times 8\]
Let us cancel the common factor 5.
\[\begin{align}
& \Rightarrow 75\%\times 80=\dfrac{{{\require{cancel}\cancel{75}}^{15}}}{{{\require{cancel}\cancel{10}}^{2}}}\times 8 \\
& \Rightarrow 75\%\times 80=\dfrac{15}{2}\times 8 \\
\end{align}\]
We can cancel the common factor 2.
\[\begin{align}
& \Rightarrow 75\%\times 80=\dfrac{15}{\require{cancel}\cancel{2}}\times {{\require{cancel}\cancel{8}}^{4}} \\
& \Rightarrow 75\%\times 80=15\times 4 \\
& \Rightarrow 75\%\times 80=60 \\
\end{align}\]
Therefore, 75% of 80 is 60.
Now, we have to find 50% of 75% of 80, that is, 50% of 60. We can write this mathematically as
$\Rightarrow 50\%\times 60$
We have to convert 50% into its number form.
$\Rightarrow 50\%\times 60=\dfrac{50}{100}\times 60$
Let us simplify the above expression by cancelling the zeroes from the numerator and the denominator.
$\begin{align}
& \Rightarrow 50\%\times 60=\dfrac{5\require{cancel}\cancel{0}}{1\require{cancel}\cancel{0}\require{cancel}\cancel{0}}\times 6\require{cancel}\cancel{0} \\
& \Rightarrow 50\%\times 60=5\times 6 \\
& \Rightarrow 50\%\times 60=30 \\
\end{align}$
Therefore, 50% of 60 is 30.
Now, let us find 20% of 50% of 75% of 80, that is, 20% of 50% of 60, or 20% of 30. We have to write the mathematical form of 20% of 30.
$\Rightarrow 20\%\times 30$
We have to convert 20% into its number form.
$\Rightarrow 20\%\times 30=\dfrac{20}{100}\times 30$
Let us simplify the above expression by cancelling the zeroes from the numerator and the denominator.
$\begin{align}
& \Rightarrow 20\%\times 30=\dfrac{2\require{cancel}\cancel{0}}{1\require{cancel}\cancel{0}\require{cancel}\cancel{0}}\times 3\require{cancel}\cancel{0} \\
& \Rightarrow 20\%\times 30=2\times 3 \\
& \Rightarrow 20\%\times 30=6 \\
\end{align}$
Therefore, 20% of 50% of 75% of 80 is $6$. So, the correct answer is “Option (b)”.
Note: Students have a chance of making a mistake by first finding 20% of 50%, then finding the result of this of 75%, and so on, that is, doing the forward operation. In these types of questions, we have to find the answer backwards. Students must learn to convert a number into its percentage and vise-versa. We can do the former operation by multiplying the number by 100.
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
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE
Which are the Top 10 Largest Countries of the World?
How do you graph the function fx 4x class 9 maths CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Why is there a time difference of about 5 hours between class 10 social science CBSE