Question

A person’s salary has increased from Rs \[7200\] to Rs \[8100\] .What is the percentage increase in his salary?
\[\left( {\text{A}} \right){\text{ }}25\% \]
\[\left( {\text{B}} \right){\text{ 18}}\% \]
\[\left( {\text{C}} \right){\text{ 16}}\dfrac{2}{3}\% \]
\[\left( {\text{D}} \right){\text{ 12}}\dfrac{1}{2}\% \]

Answer 1

Hint: To calculate percentage increase, first calculate the difference that is increased between the two numbers given in the question. Then divide the increased value by the original number and further multiply the answer by hundred. After that convert your answer into mixed fraction. The formula is given below
\[{\text{Percentage Increase = }}\dfrac{{{\text{Increased Value - Original Value}}}}{{{\text{Original Value}}}} \times 100\]

Complete step-by-step answer:
When comparing the increase in a quantity over a period of time, we first find the difference between the original value and the increased value. We then use this difference to find the relative increase against the original value and express it in terms of percentage. The formula for percentage increase is given by
\[{\text{Percentage Increase = }}\dfrac{{{\text{Increased Value - Original Value}}}}{{{\text{Original Value}}}} \times 100\] ----------- (i)
It is given to us that the person’s salary has increased from Rs \[7200\] to Rs \[8100\] .Now to find the increase of amount we have to subtract \[7200\] from \[8100\] .So,
\[Rs{\text{ }}8100 - Rs{\text{ }}7200\]
\[ \Rightarrow Rs{\text{ 900}}\]
That is the increase in the quantity is \[Rs{\text{ 900}}\] and the original quantity is \[Rs{\text{ }}7200\]
Therefore by using these values in the formula given in the equation (i) we get
\[{\text{Percentage Increase = }}\dfrac{{900}}{{7200}} \times 100\]
The zeroes of hundred and the zeroes in the denominator will cancel out and we get
\[ \Rightarrow {\text{Percentage Increase = }}\dfrac{{900}}{{72}} \times 1\]
On dividing both the numerator and the denominator by \[2\] we get
\[ \Rightarrow {\text{Percentage Increase = }}\dfrac{{450}}{{36}}\]
Again on dividing by two we get
\[ \Rightarrow {\text{Percentage Increase = }}\dfrac{{225}}{{18}}\]
Now both the numbers in the numerator and denominator are divisible by \[3\] .Therefore,
\[ \Rightarrow {\text{Percentage Increase = }}\dfrac{{75}}{6}\]
Again on dividing by \[3\] we get
\[ \Rightarrow {\text{Percentage Increase = }}\dfrac{{25}}{2}\]
To convert improper fractions to mixed fractions, we need to divide the numerator by the denominator. Then we write it in the mixed number form by placing the quotient as the whole number, the remainder as the numerator and the divisor as the denominator. Here we have \[25\] as the numerator , on dividing it by \[2\] we get
\[2\mathop{\left){\vphantom{1\begin{gathered}
  {\text{ }}25 \\
  \underline { - 24} \\
  {\text{ }}1 \\
\end{gathered} }}\right.
\!\!\!\!\overline{\,\,\,\vphantom 1{\begin{gathered}
  {\text{ }}25 \\
  \underline { - 24} \\
  {\text{ }}1 \\
\end{gathered} }}}
\limits^{\displaystyle \,\,\, {12}}\]
Therefore, \[\dfrac{{25}}{2}\] becomes \[{\text{12}}\dfrac{1}{2}\]
Hence the correct option is \[\left( {\text{D}} \right){\text{ 12}}\dfrac{1}{2}\% \]
So, the correct answer is “Option D”.

Note: Remember the formula to find the increased percentage. You should know how to convert improper fraction into a mixed fraction. Note that improper fractions are those in which the numerator is greater than the denominator and a mixed fraction is a mixture of a whole and a proper fraction.