Step 1: Calculate Ruchi's remaining chocolates

Ruchi initially had $250$ chocolates. Umesh took $100$ chocolates from her. Therefore, Ruchi's remaining chocolates are: $Ruchi_{remaining} = 250 - 100 = 150$

$250 - 100 = 150$

Step 2: Calculate Umesh's chocolates after giving to Shalaka and Marry

Umesh took $100$ chocolates. He gave $20\%$ of his chocolates to Shalaka and $35\%$ to Marry. Total percentage given away = $20\% + 35\% = 55\%$. Percentage remaining with Umesh = $100\% - 55\% = 45\%$. Number of chocolates remaining with Umesh: $Umesh_{left} = 100 \times \frac{45}{100} = 45$

$100 \times (1 - 0.20 - 0.35) = 45$

Step 3: Calculate chocolates received from Ruchi

Ruchi gave $50\%$ of her remaining chocolates ($150$) to Umesh: $Ruchi_{given} = 150 \times 0.50 = 75$

$150 \times 0.50 = 75$

Step 4: Calculate total chocolates Umesh had at the end

Adding the chocolates Umesh kept and the chocolates received from Ruchi: $Umesh_{final} = 45 + 75 = 120$

$45 + 75 = 120$