Question : A man divides his property so that his son's share to his wife's, and his wife's share to his daughter's, are in the ratio 3 : 1. If the daughter gets Rs. 10,000 less than the son, the value (in rupees) of the whole property is:
Option 1: Rs. 16,250
Option 2: Rs. 16,000
Option 3: Rs. 18,250
Option 4: Rs. 17,000
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Correct Answer: Rs. 16,250
Solution : Given: The ratio of the son's and the wife's shares is 3 : 1 i.e. 9 : 3. The ratio of the wife's and the daughter's shares is 3 : 1. So, the ratio of the three shares, son : wife : daughter = 9 : 3 : 1. Let the son's share be $9x$ units, the wife's share be $3x$ units and the daughter's share be $x$ units. The total share = $(9x+3x+x)=13x$ units The difference between the son's and daughter's shares $=(9x-x)=8x$ units So, $8x$ units are equivalent to Rs. 10,000 Therefore, $13x$ units are equivalent to ($\frac{10000×13x}{8x}$) = Rs. 16,250 So, the value of the whole property is Rs. 16250. Hence, the correct answer is Rs. 16,250.
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