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?

Explanation:-

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