Question

Mrs. Arora left one-fourth of her property for her son, two-thirds for her daughter and the
remainder for her niece. If her niece's share is? 700000, what was the worth of her total
x
property? (Hint: Let the worth of her property be ? x. Then, (- : -3) - 700000.)​

Answer 1

Let the worth of Mrs . Arora's property be x .

Then , property her son got :-

$= \frac{1}{4} \: of \: x$

$= \frac{1}{4} x$

Property her daughter got :-

$= \frac{2}{3} of \: x$

$= \frac{2}{3} x$

Sum of the property her son and daughter got :-

$= \frac{1}{4} x + \frac{2}{3}x$

$= \frac{(1 \times 3 ) + (2 \times 4)}{12}$

$= \frac{3 + 8}{12}$

$= \frac{11}{12} x$

Then , Mrs . Arora's niece's share of property :-

$= \frac{12}{12} x - \frac{11}{12}x$

$= \frac{1}{12} x$

Which means :-

$\frac{1}{12} \: of \: x = 700000$

$\frac{1}{12} x = 700000$

$x = 700000 \div \frac{1}{12}$

$x = 700000 \times \frac{12}{1}$

$x = 8400000$

Money Mrs Arora's son received :-

$= \frac{3}{12} of \: 8400000$

$= \frac{3}{12} \times 8400000$

$= 2,100,000$

Mrs . Arora's son received 2100000 .

Money Mrs . Arora's daughter received :-

$= \frac{8}{12} \: of \: 8400000$

$= \frac{8}{12} \times 8400000$

$= 5,600,000$

Mrs. Arora's daughter received 5600000 .

Therefore , the total worth of Mrs . Arora's property is 8400000 .