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What is 20% of 50% of 75% of 80?
(a) 5.5
(b) 6
(c) 8
(d) 6.5

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Last updated date: 23rd Jul 2024
Total views: 348.9k
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Answer
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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.