Explanation:

- Vandana is admitted for a \( \frac{1}{8} \) share in profits with a guaranteed profit of Rs 1,50,000.

- The remaining profit, after Vandana's guaranteed share, is to be shared between Vivek and Vikas in their original ratio of 2:3.

- The total profit for the year is Rs 9,00,000.

 Vandana's share =1/8 of Rs 9,00,000 = Rs 1,12,500.

- As her profit is less than her guaranteed Rs 1,50,000, Vivek and Vikas bear the deficiency of Rs 37,500 in the ratio 2:3.

- Vivek's share of this deficiency is \( \frac{2}{5} \times 37,500 = Rs 15,000 \).

- Remaining profit after Vandana's share is Rs 9,00,000 - Rs 1,12,500 = Rs 7,87,500 to be distributed between Vikas and Vivek.

- Vivek’s share from remaining profit is \( \frac{2}{5} \times 7,87,500 = Rs 3,15,000 \).

- Deducting his share of the deficiency: Rs 3,15,000 - Rs 15,000 = Rs 3,00,000.