Question

What is the number, $6\dfrac{1}{4}\%$ of which is 2?

Answer 1

Hint: Assume that the required number of which$6\dfrac{1}{4}\%$ is 2 is equal to x. Now, convert the mixed fraction $6\dfrac{1}{4}\%$ into the improper fraction by using the conversion $a\dfrac{b}{c}=\dfrac{\left( a\times c \right)+b}{c}$. Divide it with 100 and remove the percentage sign to get the fractional form. Take the product of this fraction with x and equate it with 2 to form a linear equation in x. Solve for the value of x to get the answer.

Complete step by step solution:
Here we have been asked to find the number whose value of $6\dfrac{1}{4}\%$ is equal to 2. Let us assume the required number as x, so mathematically we have,
$\Rightarrow 6\dfrac{1}{4}\%$ of x = 2
The term ‘of’ means multiplication in mathematics, so we have,
$\Rightarrow \left( 6\dfrac{1}{4}\% \right)\times x=2$……. (1)
Now, we need to change the given mixed fraction into the improper fraction for the calculation. Therefore, using the relation $a\dfrac{b}{c}=\dfrac{\left( a\times c \right)+b}{c}$ we can write $6\dfrac{1}{4}$ as: -
$\begin{align}
  & \Rightarrow 6\dfrac{1}{4}=\dfrac{\left( 6\times 4 \right)+1}{4} \\
 & \Rightarrow 6\dfrac{1}{4}=\dfrac{25}{4} \\
\end{align}$
Further we need to convert the percentage into the fraction for which we remove the percentage sign and divide the numerical value by 100, so we get,
$\begin{align}
  & \Rightarrow \dfrac{25}{4}\%=\dfrac{25}{4\times 100} \\
 & \Rightarrow \dfrac{25}{4}\%=\dfrac{1}{16} \\
\end{align}$
Substituting the obtained value in equation (1) we get,
$\begin{align}
  & \Rightarrow \dfrac{1}{16}\times x=2 \\
 & \Rightarrow \dfrac{x}{16}=2 \\
\end{align}$
Cross multiplying the terms of the above linear equation to find the value of x we get,
$\therefore x=32$
Hence, the required number is 32.

Note: You must remember the interconversion rules of fractions, decimals and percentages. Note that percentage is dimensionless, i.e. it has no unit and is a pure number. Remember the formula used for the conversion of a mixed fraction into an improper fraction as it is necessary for the calculations. Mathematically, the fraction $a\dfrac{b}{c}$ is equivalent to the relation $\left( a+\dfrac{b}{c} \right)$.