1. Initial Shares:
Hema's share = \( \frac{2}{5} \), Tara's share = \( \frac{3}{5} \).
2. Surrendered Shares:
Hema surrendered \( \frac{1}{3} \) of her share:
\[
\text{Hema's surrendered share} = \frac{1}{3} \times \frac{2}{5} = \frac{2}{15}.
\]
Tara surrendered \( \frac{1}{2} \) of her share:
\[
\text{Tara's surrendered share} = \frac{1}{2} \times \frac{3}{5} = \frac{3}{10}.
\]
3. Ojas's Share:
Ojas's total share = Hema's surrendered share + Tara's surrendered share:
\[
\text{Ojas's share} = \frac{2}{15} + \frac{3}{10} = \frac{4}{30} + \frac{9}{30} = \frac{13}{30}.
\]
4. Remaining Shares:
Hema's new share = \( \frac{2}{5} - \frac{2}{15} = \frac{6}{15} - \frac{2}{15} = \frac{4}{15}. \)
Tara's new share = \( \frac{3}{5} - \frac{3}{10} = \frac{6}{10} - \frac{3}{10} = \frac{3}{10}. \)
5. New Ratio:
Converting all shares to a common denominator (LCM = 30):
\[
\text{Hema's share} = \frac{4}{15} = \frac{8}{30}, \quad \text{Tara's share} = \frac{3}{10} = \frac{9}{30}, \quad \text{Ojas's share} = \frac{13}{30}.
\]
Therefore, the new ratio = \( 8 : 9 : 13 \).