Question & Answer
QUESTION

What amount is $15\%$ less than 80?

ANSWER Verified Verified
Hint: suppose the amount as a variable and form an equation with the help of the given relation in words. Percentage is a number or ratio expressed as a fraction of 100. Relation \[x\%\] of\[y\] can be given as
\[\dfrac{x}{100}\times y\]. Use the definition given here to simplify the equation formed.

Complete Step-by-Step solution:
Let us suppose the amount as ‘m’. So, it is given in the question that the amount supposed above is $15\%$ less than 80. It means we can get equation by the information in the problem as
Amount \[=\ 80-15\%\] of \[80\] …………………………………………………….(i)
We can observe the equation which suggests that the amount is less than 80 by the $15%$ of it.
So, we need to solve the relation (i) to get the amount. Hence, we know the definition of percentages as: -
We know the percentage is a number or ratio expressed as a fraction of 100 and the expression \[x\%\] of \[y\] can be given as \[\dfrac{x}{100}\times y\]. So, using the definition we get: -
Hence, using the above definition of percentage and given expression we can convert the relation $15\%$ of 80 to \[\dfrac{15}{100}\times 80\]
Amount \[=\ m\ =80-\ \dfrac{15}{100}\times 80\]
\[m\ =80-\ \dfrac{15\times 8}{10}\ =\ 80-\dfrac{2\times 8}{2}\]
\[m\ =80-\ 8\]
\[m\ =72\]
Hence, the amount is 72 which is less than 80 by $15\%$.
So, 72 is the answer to the problem.

Note: One may write the equation as Amount $+15\%$ of \[80\] = \[80\] as well from the information of the problem. But one may go wrong if he/she adds $15\%$ of 80 to 80 and equate it to Amount. So, we need to form an equation with the given information carefully. Writing the equation mathematically by using the expression given in words in the problem is the key point of the question.
One may not put ‘100’ in division to $15\%$ and hence get the amount equation as Amount \[=\ 80-15\times 80\], which is wrong. So, divide 15 by 100 and then proceed further. So, take care of it as well.