Alok went to a casino to play card game. He played 10 rounds of that game .In each round he doubled his amount and then gave Rs.x to his friend. After playing 10 rounds , he had Rs.1023 . Find the sum of the digits of the least possible value of x.
Answers
Given : Alok went to a casino to play card game. He played 10 rounds of that game .In each round he doubled his amount and then gave Rs.x to his friend. After playing 10 rounds , he had Rs.1023
To find : the sum of the digits of the least possible value of x.
Solution:
Let say He Started with Rs M
After 1st Round he had (2M - x)
After 2nd round he had = 2(2M - x) - x = 4M - 3x
After 3rd round he had = 2(4M - 3x) - x = 8M - 7x
After 10 Rounds = 2(10 + 1)M - (2(10 + 1) - 1)x
= 22M - 21x
22M - 21x = 1023
22M = 1023 + 21x
=> 22M = 22*(46) + 11 + 21x
11 + 21x = 22a
=> 21x = 11(2a - 1)
=> x = 11
least possible value of x. = 11
22M - 21x = 1023
=> M = 57
Sum of Digits of x = 1 + 1 = 2
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