The monthly salaries of Pia and Som are in the ratio of 5 : 4. From her monthly salary, gives $$\frac{{\text{3}}}{{\text{5}}}$$ to her mother, 15% towards her sister's tuition fees, 18% towards a loan and she shops with the remaining amount, which is Rs. 2100. What is the monthly salary of Som ?

Solution(By Examveda Team)

Let the monthly salary of Pia and Som be 5a and 4a respectively.
Then,
Money given by Pia to her mother
$$\eqalign{ & = 5a \times \frac{3}{5} = 3a \cr } $$
Money given by Pia as sister's tuition fees
$$\eqalign{ & = 15\% {\text{ of }}5a \cr & = \frac{{15 \times 5a}}{{100}} \cr & = \frac{{75a}}{{100}} = 0.75a \cr} $$
Money given by Pia towards loan
$$\eqalign{ & = 18\% {\text{ of }}5a \cr & = \frac{{18 \times 5a}}{{100}} \cr & = \frac{{90a}}{{100}} = 0.9a \cr & \therefore {\text{Total money given}} \cr & = 3a + 0.75a + 0.90a \cr & = 4.65a \cr & \therefore {\text{Remaining amount}} \cr & = 5a - 4.65 \cr & = 0.35a \cr & {\text{Pia have remaining amount}} \cr & = {\text{Rs}}{\text{. }}2100 \cr & 0.35a = 2100 \cr & \therefore \frac{{35a}}{{100}} = 2100 \cr & \Rightarrow a = \frac{{2100 \times 100}}{{35}} \cr & a = {\text{Rs}}{\text{. }}6000 \cr & \therefore {\text{Monthly salary of Som}} \cr & = 4a = 4 \times 6000 \cr & \,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. }}24000 \cr} $$