Question

What percent of \[\dfrac{2}{7}\]is \[\dfrac{1}{{35}}\]?
a). \[2.5\% \]
b). \[10\% \]
c). \[25\% \]
d). \[20\% \]

Answer 1

Hint: We will suppose the required percentage to be \[x\]. Now, according to the question we are given, \[x\% \]of \[\dfrac{2}{7}\] is \[\dfrac{1}{{35}}\]. After that, we will frame the equation with the given information. i.e. we will find the value of \[x\% \] of \[\dfrac{2}{7}\] and then equate it with the given number. With the equation obtained, we will then solve for \[x\] and then find the value of \[x\], which will be the required percentage.

Complete step-by-step solution:
Let us suppose the required percentage is \[x\].
Now, according to the question,
We have,
\[x\% \] of \[\dfrac{2}{7}\]is \[\dfrac{1}{{35}}\]
Now, finding \[x\% \]of \[\dfrac{2}{7}\].
\[x\% \] of \[\dfrac{2}{7} = \dfrac{x}{{100}}\]of \[\dfrac{2}{7}\]
\[ = \dfrac{x}{{100}} \times \dfrac{2}{7}\]
\[ = \dfrac{x}{{50}} \times \dfrac{1}{7}\] (Dividing by 2)
\[ = \dfrac{x}{{350}}\]
Hence, \[x\% \] of \[\dfrac{2}{7} = \dfrac{x}{{350}}\] ---(1)
Also, according to question, \[x\% \] of \[\dfrac{2}{7} = \dfrac{1}{{35}}\] ---(2)
Now, equating (1) and (2), we get,
\[\dfrac{x}{{350}} = \dfrac{1}{{35}}\]
\[\Rightarrow x = \dfrac{{350}}{{35}}\] (cross multiplying)
\[\Rightarrow x = 10\]
Hence, the required percentage is \[10\% \].
Which means, \[10\% \]of \[\dfrac{2}{7}\] is \[\dfrac{1}{{35}}\].
So, the correct answer is (b).

Note: In these types of questions, we need to take care of the language. i.e. we need to read the question carefully and then frame the equation for the problem. Not reading the question correctly and not understanding the language of the question will result in failure of the answer. We usually misunderstand the problems of this type and then frame the equations according to that. So, taking care of all these things, we need to solve the question.