I take a four digit number and subtract from it the sum of its digits In the result I strike off one...........

Quantitative Aptitude ( CCS) Number System

I take a four-digit number and subtract from it the sum of its digits. In the result I strike off one of the digits and the remaining three digits of the result are 2, 4 and 6 (not necessarily in that order). Find the digit struck off by me.

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Explanation:

Let us assume the four digit number as wxyz. Then in base system 10 it can written as 1000w + 100x + 10y + z.

Now given that,
wxyz = 1000w + 100x + 10y + z - (w + x + y + z) = 999w + 99x + 9y which is a multiple of 9
Hence the sum of digits must be a multiple of 9.

Hence 2 + 4 + 6 + x is equal to either 9, 18, 27 ...
But if the sum is equal to 9 then x is negative number.

Therefore x = 6.

Hence, option 2 is the correct answer.