Question

Solve the following:
Anima left one-half of her property to her daughter, one-third to her son and donated the rest to an educational institute. If the donation was worth Rs. 100000, how much money did Anima have?

Answer 1

Let Anima's property be $Rs.x$.
Property left for her daughter =Rs. $\frac{x}{2}$
Remaining property=$x-\frac{x}{2}=\frac{2x-x}{2}=Rs.\frac{x}{2}$
property left for her son =$\frac{1}{3}$ of remaining property= $\frac{1}{3}\times \frac{x}{2}=Rs.\frac{x}{6}$
Remaining property=$[x-(\frac{x}{2}+\frac{x}{6})]=x-\left(\frac{3x+x}{6}\right)=\frac{6x-4x}{6}=\frac{2x}{6}=Rs.\frac{x}{3}$
Since, the remaining property donated to an eduactional institute.
But donation property= Rs. 100000
$\therefore \frac{x}{3}=100000\Rightarrow x=300000$
Hence, Anima had $Rs.300000$