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Question

Answers

(a) 20

(b) 25

(c) 32

(d) 40

Answer
Verified

Hint:Percentage is a number expressed as a fraction of 100. Find the \[40\%\] of 80 by multiplying 80 by 40 and hence divide the result by 100, as per the definition of percentage. So, \[x\%\] of y can be given as \[\dfrac{x\times y}{100}\].

__Complete step-by-step answer:__

As we know, percentage is a number or ratio expressed as a fraction of 100. It is often denoted using percent sign %. In other words, a percentage is a part of a whole expressed in hundredths.

Now, if we need to calculated \[x\%\] of any number \['y'\] then we have to find a part of \['y'\], which is \[x\] times of the fraction\[\dfrac{y}{100}\].

It means \[x\%\] of any number \[y\] can be calculated by doing product of \[\dfrac{x}{100}\] and y or by doing product of \[x\] and \[\dfrac{y}{100}\].

Now, coming to the question, as we need to find \[40\%\] of 80. It means we need to calculate \[{{\left( \dfrac{40}{100} \right)}^{th}}\] part of the number 80. So, we can calculate the number, which is \[40\%\] of 80, by finding the product of both, that is by calculating the product of 80 and \[\dfrac{40}{100}\], we can get the required number.

Hence, \[40\%\] of 80 is given as

\[40\%\text{ of }80=40\times \dfrac{80}{100}\]

We can divide 40 by 10 and 100 by 10, to get the above expression in simplified form. So, we get \[40\%\text{ of }80=4\times \dfrac{80}{10}\]

Now, we can divide 80 by 10 and 10 by 10 in numerator and denominator respectively. So, we get \[40\%\text{ of }80=4\times 8=32\]

Hence, 32 is the number which is \[40\%\text{ of }80\].

So, option (c) is the correct answer.

Note: One may go wrong if he/she divides 80 by 40 and hence, multiply it by 100. As one may think that that percentage means we need to multiply by 100, which is wrong. So, don’t make these mistakes with these kinds of questions.

Another approach to solve the question would be that

Number 100 consist of 40

1 consist of \[\dfrac{40}{100}\]

80 will consist of \[\begin{align}

& \dfrac{40}{100}\times 80 \\

& =32. \\

\end{align}\]

As we know, percentage is a number or ratio expressed as a fraction of 100. It is often denoted using percent sign %. In other words, a percentage is a part of a whole expressed in hundredths.

Now, if we need to calculated \[x\%\] of any number \['y'\] then we have to find a part of \['y'\], which is \[x\] times of the fraction\[\dfrac{y}{100}\].

It means \[x\%\] of any number \[y\] can be calculated by doing product of \[\dfrac{x}{100}\] and y or by doing product of \[x\] and \[\dfrac{y}{100}\].

Now, coming to the question, as we need to find \[40\%\] of 80. It means we need to calculate \[{{\left( \dfrac{40}{100} \right)}^{th}}\] part of the number 80. So, we can calculate the number, which is \[40\%\] of 80, by finding the product of both, that is by calculating the product of 80 and \[\dfrac{40}{100}\], we can get the required number.

Hence, \[40\%\] of 80 is given as

\[40\%\text{ of }80=40\times \dfrac{80}{100}\]

We can divide 40 by 10 and 100 by 10, to get the above expression in simplified form. So, we get \[40\%\text{ of }80=4\times \dfrac{80}{10}\]

Now, we can divide 80 by 10 and 10 by 10 in numerator and denominator respectively. So, we get \[40\%\text{ of }80=4\times 8=32\]

Hence, 32 is the number which is \[40\%\text{ of }80\].

So, option (c) is the correct answer.

Note: One may go wrong if he/she divides 80 by 40 and hence, multiply it by 100. As one may think that that percentage means we need to multiply by 100, which is wrong. So, don’t make these mistakes with these kinds of questions.

Another approach to solve the question would be that

Number 100 consist of 40

1 consist of \[\dfrac{40}{100}\]

80 will consist of \[\begin{align}

& \dfrac{40}{100}\times 80 \\

& =32. \\

\end{align}\]

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