Archive
20th of March 2017
Mathematics
Q:

1. When 1099 – 99 is evaluated, then what is the sum of the digits?

Sahil Kumar Sahoo - CBSE - Class X

Monday, March 20, 2017 at 18:18:PM

A:

begin mathsize 16px style Observe space that space 10 to the power of 99 space is space just space 1 space followed space by space 99 space zeros. space
When space you space subtract space 99 comma space from space 100000....00 comma space you space must space borrow space from space every space column space all space the space way space to space the space left. space
So space now comma space every space 0 space changes space into space straight a space 9 comma space except space the space last space zero comma space which space is space 10 space after space the space borrow. space
That space means space you space have space 98 space nines. space space
And space the space 1 space in space the space front space becomes space straight a space 0.
Performing space the space subtraction space in space the space one apostrophe straight s space place comma space we space get space 10 space minus space 9 space equals space 1 space
Performing space the space subtraction space in space the space ten apostrophe straight s space place comma space we space get space 9 space minus space 9 space equals space 0
Performing space the space subtraction space all space the space way space across comma space we space get space 9 space minus space 0 space equals space 9 space left parenthesis same space thing space 97 space times right parenthesis space
Sum space up space 1 space plus space 0 space plus space 97 cross times 9 equals 1 plus 873 equals 874 end style

Monday, March 20, 2017 at 18:27:PM