Amitabh picks a random integer between 1 and 999, doubles it and gives the result to Sashi. Each time Sashi gets a number from Amitabh, he adds 50 to the number, and gives the result back to Amitabh, who doubles the number again. The first person, whose result is more than 1000, loses the game. Let 'X' be the smallest initial number that results in a win for Amitabh. The sum of the digit of 'X' is:

Explanation:-

Assume x is the required number.
Step 1 Amitabh 2x Sashi 2x + 50
Step 2 Amitabh 4x + 100. Sashi 4x + 150
Step 3 Amitabh 8x + 300. Sashi 8x + 350
Step 4 Amitabh 16x + 700 Sashi 16x + 750
Now, 16x + 750 > 1000
And, x can be 16
So 7 is the sum