Ram left $$\frac{1}{3}$$ of his property to his widow and $$\frac{3}{5}$$ of the remainder to his daughter. He gave the rest to his son who received Rs. 6,400. How much was his original property worth?
a) Rs. 16,000
b) Rs. 24,000
c) Rs. 30,000
d) Rs. 32,000

Answer: b
Explanation:
$$\eqalign{ & {\text{Let}}\,{\text{total}}\,{\text{property}}\,{\text{of}}\,{\text{Ram}} = x \cr & {\text{His}}\,{\text{widow}}\,{\text{gets}} \cr & \frac{1}{3}\,of\,x = \frac{x}{3} \cr & {\text{His}}\,{\text{daughter}}\,{\text{gets}}\, \cr & = \frac{3}{5}\,of\,\left[ {x – {\frac{x}{3}} } \right] \cr & = \frac{3}{5} \times {\frac{{2x}}{3}} \cr & = \frac{{2x}}{5} \cr & {\text{His}}\,{\text{son}}\,{\text{gets}}\,{\text{his}}\,{\text{rest}}\,{\text{property}} \cr & {\text{His}}\,{\text{son’s}}\,{\text{property}} \cr & = x – \left[ { {\frac{x}{3}} + {\frac{{2x}}{5}} } \right] \cr & 6400 = x – {\frac{{11x}}{{15}}} \cr & 6400 = \frac{{ {15x – 11x} }}{{15}} \cr & 4x = 6400 \times 15 \cr & x = 1600 \times 15 \cr & x = 24000 \cr & {\text{Total}}\,{\text{Property}} = 24000 \cr} $$