Question : Ram left $\frac{1}{3}$rd of his property to his wife and $\frac{3}{5}$th 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?
Option 1: Rs. 16,000
Option 2: Rs. 32,000
Option 3: Rs. 24,000
Option 4: Rs. 1,600
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Correct Answer: Rs. 24,000
Solution :
Let the total property of Ram be worth Rs. $x$.
Given: His wife gets Rs. $\frac{x}{3}$
His daughter gets = $\frac{3}{5}$ of $(x–\frac{x}{3})$ = $\frac{3}{5}\times \frac{2x}{3}$ = $\frac{2x}{5}$
His son gets = $x - (\frac{x}{3} + \frac{2x}{5})$
So, 6400 = $x - \frac{11x}{15}$
or, 6400 = $\frac{15x–11x}{15}$
or, $4x$ = 6400 × 15
or, $x$ =1600 ×15 = 24,000
So, the total property of Ram is worth Rs. 24,000.
Hence, the correct answer is Rs. 24,000.
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