Question

Solve the following:
\[6\dfrac{1}{4}\%\] of which number is 2?

Answer 1

Hint: We are given a question having the percentage of a certain number which gives a value as 2. And we are asked to find that particular number. Let the unknown number be ‘x’. We will first write the mathematical expression of the same and we get, \[6\dfrac{1}{4}\%\times x=2\]. We will then solve this expression and write the expression in terms of ‘x’. Then, we will simplify the expression and we will get the value of ‘x’. Hence, we will have the required number.

Complete step by step answer:
According to the given question, we are asked to find a number whose \[6\dfrac{1}{4}\%\] gives a value as 2.
Let the unknown number be ‘x’.
We will first write the mathematical expression of the given statement and so we have,
\[6\dfrac{1}{4}\%\times x=2\]
We will now open up the terms and simplify them and find the value of \[x\]. So, we have,
\[\Rightarrow \dfrac{25}{4\times 100}\times x=2\]
Dividing 100 by 25, we get the expression as,
\[\Rightarrow \dfrac{1}{4\times 4}\times x=2\]
We will now write the expression in terms of \[x\] and so we will have the expression as,
\[\Rightarrow x=2\times 4\times 4\]
Multiplying the terms in the above expression, we get the value of ‘x’ as,
\[\Rightarrow x=32\]
Therefore, the required number which satisfies the given statement is 32.

Note: The percentage given in the above solution, which is, \[6\dfrac{1}{4}\%\] should be opened as \[\dfrac{25}{4\times 100}\] with 100 in the denominator and not in the numerator like this, \[\dfrac{25}{4}\times 100\] else the solution will get wrong. Also, the obtained can be checked whether it is correct or not by substituting the value in the expression.