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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?
Options:
A .  Rs. 16,000
B .  Rs. 24,000
C .  Rs. 30,000
D .  Rs. 32,000
Answer: Option B
$$\eqalign{
& {\text{Let}}\,{\text{total}}\,{\text{property}}\,{\text{of}}\,{\text{Ram}} = x \cr
& {\text{His}}\,{\text{widow}}\,{\text{gets}} \cr
& \frac{1}{3}\,of\,x = \frac{x}{3} \cr
& {\text{His}}\,{\text{daughter}}\,{\text{gets}}\, \cr
& = \frac{3}{5}\,of\,\left[ {x - {\frac{x}{3}} } \right] \cr
& = \frac{3}{5} \times {\frac{{2x}}{3}} \cr
& = \frac{{2x}}{5} \cr
& \cr
& {\text{His}}\,{\text{son}}\,{\text{gets}}\,{\text{his}}\,{\text{rest}}\,{\text{property}} \cr
& {\text{His}}\,{\text{son's}}\,{\text{property}} \cr
& = x - \left[ { {\frac{x}{3}} + {\frac{{2x}}{5}} } \right] \cr
& 6400 = x - {\frac{{11x}}{{15}}} \cr
& 6400 = \frac{{ {15x - 11x} }}{{15}} \cr
& 4x = 6400 \times 15 \cr
& x = 1600 \times 15 \cr
& x = 24000 \cr
& {\text{Total}}\,{\text{Property}} = 24000 \cr} $$

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