Question

What is \[12\dfrac{1}{2}\% \]of Rs.50 is equal to:
A. Rs.6.25
B. Rs.6.15
C. Rs.6.75
D. Rs.6.45

Answer 1

Hint: We use the concept of percentage to find the percentage of given amount. Convert the percentage from mixed fraction form to proper fraction form. Then apply that percentage to the given amount. Write the final answer in decimal form.
* Percentage is a part of a whole or complete. Percentage is always greater than or equal to 0% and always less than or equal to 100%.
* General form of a mixed fraction is \[a\dfrac{b}{c}\] and it can be converted into proper fraction as \[a\dfrac{b}{c} = \dfrac{{a \times c + b}}{c}\]
* We can write \[m\% \] of \[x\]as\[\dfrac{m}{{100}}x\]
* Any number that has a denominator term like \[{10^n}\] can be converted into decimal form by placing the decimal at the nth place starting from the right side. So, the term in the numerator terminates after ‘n’ places of decimals.

Complete step by step solution:
We are given the amount of Rs.50
We have to calculate \[12\dfrac{1}{2}\% \] of Rs.50
Firstly we convert the mixed fraction in percentage in proper fraction in percentage.
Mixed fraction is \[12\dfrac{1}{2}\]................… (1)
Use the formula of converting mixed fraction to proper fraction i.e. \[a\dfrac{b}{c} = \dfrac{{a \times c + b}}{c}\]
We can write the mixed fraction in equation (1) as
\[ \Rightarrow 12\dfrac{1}{2} = \dfrac{{12 \times 2 + 1}}{2}\]
Multiply the terms in the numerator of RHS
\[ \Rightarrow 12\dfrac{1}{2} = \dfrac{{24 + 1}}{2}\]
Add the terms in the numerator of RHS
\[ \Rightarrow 12\dfrac{1}{2} = \dfrac{{25}}{2}\]
So, the mixed fraction in equation (1) becomes \[\dfrac{{25}}{2}\]
\[ \Rightarrow 12\dfrac{1}{2}\% = \dfrac{{25}}{2}\% \]
Divide 25 by 2 to convert percentage in decimal form
\[ \Rightarrow 12\dfrac{1}{2}\% = 12.5\% \].....................… (2)
Now we have to calculate \[12\dfrac{1}{2}\% \] of Rs.50
This means we have to calculate \[12.5\% \] of Rs.50
We know \[m\% \] of \[x\] is given by\[\dfrac{m}{{100}}x\]
\[ \Rightarrow 12.5\% \] of Rs.50 \[ = \dfrac{{12.5}}{{100}} \times 50\]
Cancel same terms or factors from both numerator and denominator of the fraction in RHS
\[ \Rightarrow 12.5\% \] of Rs.50 \[ = \dfrac{{12.5 \times 5}}{{10}}\]
Multiply the values in the numerator of RHS
\[ \Rightarrow 12.5\% \] of Rs.50 \[ = \dfrac{{62.5}}{{10}}\]
Now convert the fraction into decimal form using the number of multiples of 10 given in the denominator. Compare the value with \[{10^n}\]
Since the value of n is 1, we will have two digits after the decimal point.
\[ \Rightarrow 12.5\% \] of Rs.50 \[ = 6.25\]
\[\therefore 12.5\% \] of Rs.50 is Rs.6.25

\[\therefore \]Option A is correct.

Note: Students might make mistakes in calculation as they get confused with both mixed fraction and decimal, students are advised to proceed step by step, first convert into proper fraction and then into decimal form.
Also, when converting fraction into percentage, we multiply the fraction by 100. Also, students might make mistakes while converting mixed fraction to proper fraction as they tend to multiply the whole number with a numerator and then add the denominator. Keep in mind we multiply the whole number to number in denominator and then add the number in numerator which becomes our new numerator.