Question

What percent of 80 is 56?

Answer 1

Hint: We solve this problem by using the percentages. We assume the required percentage as some variable and develop an equation based on the given numbers and find the variable value which is the required percentage. We use the condition that if $a$ percent of $b$ is $c$ then the mathematical equation is given as,
$\Rightarrow {\displaystyle \frac{a}{100}}\times b=c$

Complete step-by-step solution:
We are asked to find what percent of 80 is 56.
Let us assume that the required percentage as ${}^{\prime }{x}^{\prime }$
Now, we can reframe the given statement as $x$ percent of 80 is 56.
We know that the condition of percentages that is if $a$ percent of $b$ is $c$ then the mathematical equation is given as,
$\Rightarrow {\displaystyle \frac{a}{100}}\times b=c$
By using this condition to above reframed statement then we get the mathematical equation as,
$\begin{array}{rl}& \Rightarrow {\displaystyle \frac{x}{100}}\times 80=56\\ & \Rightarrow {\displaystyle \frac{8x}{10}}=56\end{array}$
Now, by cross multiplying the terms from LHS to RHS then we get,
$\begin{array}{rl}& \Rightarrow x=56\times {\displaystyle \frac{10}{8}}\\ & \Rightarrow x=7\times 10\\ & \Rightarrow x=70\mathrm{\%}\end{array}$
Therefore, we can conclude that the required percentage is 70% that is 70% of 80 is 56.

Note: We can solve this problem in another method.
We are asked to find what percent of 80 is 56.
We know that percent is calculated to 100.
So, let us assume that 80 is divided into 100 parts.
Let us assume that value of each part as $a$ then we get,
$\begin{array}{rl}& \Rightarrow a={\displaystyle \frac{80}{100}}\\ & \Rightarrow a={\displaystyle \frac{4}{5}}\end{array}$
Now, we know that if 80 is divided into 100 parts then the number of parts having the same value that gets 56 is the required percentage.
Let us assume that $x$ parts of value equal to $a$ forms 56 then we get,
$\Rightarrow x\times {\displaystyle \frac{4}{5}}=56$
Now, by cross multiplying the terms from LHS to RHS then we get,
$\begin{array}{rl}& \Rightarrow x=56\times {\displaystyle \frac{5}{4}}\\ & \Rightarrow x=14\times 5\\ & \Rightarrow x=70\mathrm{\%}\end{array}$
Therefore, we can conclude that the required percentage is 70% that is 70% of 80 is 56.