Correct Answer - Option 1 : 14.28%
Given:
Increase in income = 28.56%
Deduction in Income = 33.33%
Difference between increased income and present income = Rs. 3300
Concept Used:
In this type of questions, Percentage values should be changed into Fraction values.
Formula Used:
To change given % in fraction, we first convert the % into mixed fraction value.
\({\rm{Fraction\;value}} = \frac{{{\rm{Percentage\;given}}}}{{100}}\)
Representation done by fraction values will be taken as,
\({\rm{Fraction\;value}} = \frac{{{\rm{Increased\;value}}}}{{{\rm{Initial\;value}}}}\)
\({\rm{Percentage\;less}} = \frac{{{\rm{Difference\;between\;Initial\;and\;final\;value}}}}{{{\rm{Initial\;Value}}}}\; \times 100\)
Calculation:
Using Formula and concept,
\(\begin{array}{l} 28.56{\rm{\% }} = 28\frac{4}{7} = \frac{{200}}{7}\% \\ 33.33{\rm{\% }} = 33\frac{1}{3} = \frac{{100}}{3}\% \\ {\rm{Fraction\;value\;of\;}}28.56{\rm{\% }} = \frac{{\frac{{200}}{7}}}{{100}} = \frac{{200}}{{700}} = \frac{2}{7}\\ {\rm{Fraction\;Value\;of\;}}33.33{\rm{\% }} = \frac{{\frac{{100}}{3}}}{{100}} = \frac{{100}}{{300}} = \frac{1}{3}\; \end{array}\)
Suppose Income of Sumit be 7 Units then after increase of 2 Units
New Income = 7 + 2 = 9 Units
Deduction in salary in the ratio of 1/3
\({\rm{deducted\;amount}} = \frac{1}{3}\; \times 9 = 3\;{\rm{Units}}\)
New Salary = 9 – 3 = 6 Units
Difference in Initial and final Salary = 7 - 6 = 1 Unit
\({\rm{Final\;SalaryPercentage\;less\;than\;the\;Initial\;salary}} = \frac{1}{7}\; \times 100 = 14.28\% \)
∴ Final Salary of Sumit is 14.28% less than the Initial Salary.
