Question

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

Answer 1

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
$\Rightarrow 75\mathrm{\%}\times 80$
We know that to convert a percentage into a number, we have to divide that percentage by 100. Therefore, 75% can be written as ${\displaystyle \frac{75}{100}}$ . Hence, the above expression becomes
$\Rightarrow 75\mathrm{\%}\times 80={\displaystyle \frac{75}{100}}\times 80$
Let us cancel the zeroes from the numerator and the denominator.
$$\Rightarrow 75\mathrm{\%}\times 80={\displaystyle \frac{75}{10\text{cancel}0}}\times 8\text{cancel}0$$
We can write the result of the above simplification as
$$\Rightarrow 75\mathrm{\%}\times 80={\displaystyle \frac{75}{10}}\times 8$$
Let us cancel the common factor 5.
$$\begin{array}{rl}& \Rightarrow 75\mathrm{\%}\times 80={\displaystyle \frac{{\text{cancel}75}^{15}}{{\text{cancel}10}^2}}\times 8\\ & \Rightarrow 75\mathrm{\%}\times 80={\displaystyle \frac{15}{2}}\times 8\end{array}$$
We can cancel the common factor 2.
$$\begin{array}{rl}& \Rightarrow 75\mathrm{\%}\times 80={\displaystyle \frac{15}{\text{cancel}2}}\times {\text{cancel}8}^4\\ & \Rightarrow 75\mathrm{\%}\times 80=15\times 4\\ & \Rightarrow 75\mathrm{\%}\times 80=60\end{array}$$
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
$\Rightarrow 50\mathrm{\%}\times 60$
We have to convert 50% into its number form.
$\Rightarrow 50\mathrm{\%}\times 60={\displaystyle \frac{50}{100}}\times 60$
Let us simplify the above expression by cancelling the zeroes from the numerator and the denominator.
$\begin{array}{rl}& \Rightarrow 50\mathrm{\%}\times 60={\displaystyle \frac{5\text{cancel}0}{1\text{cancel}0\text{cancel}0}}\times 6\text{cancel}0\\ & \Rightarrow 50\mathrm{\%}\times 60=5\times 6\\ & \Rightarrow 50\mathrm{\%}\times 60=30\end{array}$
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.
$\Rightarrow 20\mathrm{\%}\times 30$
We have to convert 20% into its number form.
$\Rightarrow 20\mathrm{\%}\times 30={\displaystyle \frac{20}{100}}\times 30$
Let us simplify the above expression by cancelling the zeroes from the numerator and the denominator.
$\begin{array}{rl}& \Rightarrow 20\mathrm{\%}\times 30={\displaystyle \frac{2\text{cancel}0}{1\text{cancel}0\text{cancel}0}}\times 3\text{cancel}0\\ & \Rightarrow 20\mathrm{\%}\times 30=2\times 3\\ & \Rightarrow 20\mathrm{\%}\times 30=6\end{array}$
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.