A person saves $$33\frac{1}{3}\% $$  of his income. If the saving increases by 22% and the expenditure increases by 10%, then the percentage increase in his income is:

Solution(By Examveda Team)

$$\eqalign{ & 33\frac{1}{3}\% = \frac{1}{3} \cr & {\text{Let income}} = 300 \cr & {\text{Saving}} = 100 \cr & {\text{Expenditure}} = 300 - 100 = 200 \cr} $$
\[\begin{array}{*{20}{c}} {}&{{\text{Income}}}& = &{{\text{Expenditure}}}& + &{{\text{Saving}}} \\ {{\text{Old}} \to }&{300}& = &{200}& + &{100} \\ {}&{}&{}&{\,\,\,\,\,\,\,\,\,\,{ \downarrow ^{ + 10\% }}}&{}&{\,\,\,\,\,\,\,\,\,\,{ \downarrow ^{ + 22\% }}} \\ {{\text{New}} \to }&x& = &{220}& + &{122} \end{array}\]
$$\eqalign{ & x = 220 + 122 = 342 \cr & {\text{Increase}} = 342 - 300 = 42 \cr & {\text{Increase }}\% = \frac{{42}}{{300}} \times 100 = 14\% \cr} $$