Question

What percentage of \[Rs.250\] is \[Rs.25\]?

Answer 1

Hint: We need to find the percentage such that \[Rs.25\] is that percent of \[Rs.250\]. We will suppose that percentage to be \[x\]. Then, we will frame an equation according to the given condition. Then, according to the question, We are given that \[x\% \] of \[Rs.250\] is equal to \[Rs.25\]. Also, we know
\[1\% = \dfrac{1}{{100}}\]
i.e. \[1\% \]of \[A\]\[ = \dfrac{1}{{100}}\] of \[A\]
We will then solve \[x\% \] of \[Rs.250\] and then equate it with \[Rs.25\].

Complete step-by-step solution:
Let us suppose the percentage to be \[x\].
Now, according to the question, we are given
\[x\% \] of \[Rs.250 = Rs.25\]
We now, solve the Left Hand Side first i.e. \[x\% \] of \[Rs.250\]
\[x\% \] of \[Rs.250\]\[ = x \times \dfrac{1}{{100}}\]of \[Rs.250\]
 \[ = \dfrac{x}{{100}}\]of \[Rs.250\]
 \[ = \dfrac{x}{{100}} \times Rs.250\]
\[ = Rs.\dfrac{{250x}}{{100}}\]
 \[ = Rs.\dfrac{{5x}}{2}\] (Simplifying \[\dfrac{{250}}{{100}} = \dfrac{5}{2}\])
\[\therefore x\% \] of \[Rs.250 = Rs.\dfrac{{5x}}{2}\] ----(1)
Also, \[x\% \] of \[Rs.250 = Rs.25\] ----(2)
So, from (1) and (2), we get
\[Rs.\dfrac{{5x}}{2} = Rs.25\]
\[\Rightarrow Rs.\dfrac{{5x}}{2} = Rs.\dfrac{{25}}{1}\]
\[\Rightarrow Rs.5x = Rs.(25 \times 2)\] (Cross Multiplying)
 \[\Rightarrow Rs.5x = Rs.50\]
 \[\Rightarrow x = \dfrac{{Rs.50}}{{Rs.5}}\]
 \[\therefore x = 10\]
Hence, we get \[\therefore x = 10\]
i.e. , we get,
\[10\% \] of \[Rs.250\] is \[Rs.25\]

Note: First of all, we need to be very careful while we are shifting the terms from one side to another i.e. we need to take care of the signs which change when we shift the terms. Also, we are given Rs. in this question, so we should not forget to write the units i.e. Rs. And, we need to find the percentage here, so with percentage we are supposed to add the% symbol. The equations are to be framed after reading the question very carefully. If the question is misread, then the equation to be framed will be wrong which will lead to the wrong answer.