 # Anima left one-half of her property

Question:

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?

Solution:

Let Anima's property be $₹ x$.

Property left for her daughter $=₹ \frac{x}{2}$

Remaining property $=x-\frac{x}{2}=\frac{2 x-x}{2}=₹ \frac{x}{2}$

Property left for her son $=\frac{1}{3}$ of remaining property $=\frac{1}{3} \times \frac{x}{2}=₹ \frac{x}{6}$

Remaining property $=\left[x-\left(\frac{x}{2}+\frac{x}{6}\right)\right]=x-\left(\frac{3 x+x}{6}\right)=\frac{6 x-4 x}{6}=\frac{2 x}{6}=₹ \frac{x}{3}$

Property left for her son $=\frac{1}{3}$ of remaining property $=\frac{1}{3} \times \frac{x}{2}=₹ \frac{x}{6}$

Remaining property $=\left[x-\left(\frac{x}{2}+\frac{x}{6}\right)\right]=x-\left(\frac{3 x+x}{6}\right)=\frac{6 x-4 x}{6}=\frac{2 x}{6}=₹ \frac{x}{3}$

Since, the remaining property donated to an educational institute. But donation property $=₹ 100000$

$\therefore \quad \frac{x}{3}=100000 \Rightarrow x=300000$

Hence, Anima had $₹ 300000$.