A father divides his estate among his three sons, in such a manner, that:
The first has Rs.10000 less than half of the whole;
The second has Rs.8000 less than one third of the whole;
The third has Rs.6000 less than one fourth of the whole;
What is the value of the estate?
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The total value of the estate is Rs. 2,88,000.
Given:
Share of property that each son gets:
The first son = x/2 - 10,000
The second son = x/3 - 8,000
The third son = x/4 - 6,000
To Find:
The total value of the estate.
Solution:
Let us assume that the total value of the estate is Rs. x
According to the given conditions, the property share each son gets is:
The first son = x/2 - 10,000
The second son = x/3 - 8,000
The third son = x/4 - 6,000
Then,
(x/2 - 10,000) + (x/3 - 8,000) + (x/4 - 6,000) = x
⇒ (x - 20,000)/2 + (x - 24,000)/3 + (x - 24,000)/4 = x
⇒ (12x - 2,40,000+ 8x - 1,92,000 + 6x - 1,44,000)/24 = x
⇒ 26x - 5,76,000 = 24x
⇒ -5,76,000 = -2x
⇒ x = 2,88,000
∴ The total value of the estate is Rs. 2,88,000.
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