Question

What percentage of 56 is 42?

Answer 1

Hint: This type of question depends on the basic concept of percentage. As we know that the percentage is a number or ratio which can be expressed as a fraction with denominator 100 in other words we can say a part per 100. The word percent means per 100. Also we know that the symbol “%” is used to represent percentage. Hence when we consider \[x\%\] then it says that the \[x\] numbers are per 100. It can also be expressed as \[\dfrac{x}{100}\].

Complete step by step solution:
Now, we have to find out the percentage of 56 is 42.
For this, we suppose that the \[x\] percentage of 56 is 42 that is \[x\%\] of 56 is 42.
\[\Rightarrow x\%\text{ of }56=42\]
We know that, here “of” will represent multiplication operation and hence, we can write
\[\Rightarrow x\%\times 56=42\]
Now we can write \[x\%\] as \[\dfrac{x}{100}\]so we get,
\[\Rightarrow \left( \dfrac{x}{100} \right)\times 56=42\]
\[\begin{align}
  & \Rightarrow x=\dfrac{42\times 100}{56} \\
 & \Rightarrow x=\dfrac{3\times 100}{4} \\
 & \Rightarrow x=3\times 25 \\
 & \Rightarrow x=75 \\
\end{align}\]
Hence, 75 percent of 56 is 42 that is 75% of 56 is 42.

Note: In this type of question students may make mistakes in calculation of numbers as well as in representing \[x\%\] as \[\dfrac{x}{100}\]. Students have to take care in performing multiplication and division especially when transferring numbers from left side to right side. Also, students have to take note that the word percentage and percent are closely related to each other. Per cent is accompanied with a specific number.