the digit 1 is attached to the right of a 3 digit number making it a 4 digit number which is 7777 more than?

Question

the given number .The sum of the digits of the number is
a)23
b)18
c)17
d)16

Answer 1

let the three digit number be "abc" (in the usual representation)

then we have abc1 = abc+7777

or, 10abc+1 = abc+7777
or, 9abc = 7776
or abc = 864 where a=8, b=6 and c=4

hence the sum = 8+6+4 = 18

note: recent olympiad problem!

Answer 2

If xyz is the number then, xyz1 - xyz = 7777

1000x + 100y + 10z + 1 - 100x - 10y - z = 7777

900x + 90y + 9z = 7776

100x + 10y + z = 864

So the number is 864 and the sum of the digits is: 8 + 6 + 4 = 18

The right answer is (b)

Answer 3

1000a+100b+10c+1-(100a+10b+c)=7777
900a+90b+9c+1=7777
9(100a+10b+c)=7776
100a+10b+c=864
a=8
b=6
c=4
a+b+c=18

"b" is the correct answer.