The respective ratio between the monthly salaries of Rene and Som is 5 : 3. Out of her salary Rene gives $$\frac{{\text{1}}}{{\text{6}}}$$ th as rent, $$\frac{{\text{1}}}{{\text{5}}}$$ th to her mother, 30% as her education loan and keeps 25% aside for miscellaneous expenditure. Remaining Rs. 5000 she keeps as savings. What is Som's monthly salary ?

Solution(By Examveda Team)

Let the monthly salaries of Rene and Som be 5a and 3a respectively.
Money spent by Rene
$$ = \left( {\frac{1}{6}{\text{of }}5a + \frac{1}{5}{\text{of }}5a + 30\% {\text{ of }}5a + 25\% {\text{ of }}5a} \right)$$
According to given information
$$ \Rightarrow 5a - $$ $$\left[ {5a \times \frac{1}{6} + 5a \times \frac{1}{5} + 5a \times \frac{3}{{10}} + \frac{{5a}}{4}} \right] = $$       $$ 5000$$
$$\eqalign{ & \Rightarrow 5a - \left[ {\frac{{5a}}{6} + a + \frac{{3a}}{2} + \frac{{5a}}{4}} \right] = 5000 \cr & \Rightarrow 5a - \left( {\frac{{55a}}{{12}}} \right) = 5000 \cr & \Rightarrow 60a - 55a = 60000 \cr & \Rightarrow a = 12000 \cr & \therefore {\text{Som's salary}} \cr & = 3 \times 12000 \cr & = {\text{Rs}}{\text{. }}36000 \cr} $$