Let , S = 10a + b
If “S” is divisible by 7 then if we substract or add any multiple of “7” to “S ” then resultant number will still be divisible by “7”
So we get,
S -7a is divisible by 7
So 10a+b-7a divisible by 7
3a+b also divisible by 7
If we multiply it by 5 , then resultant number will also be divisible by 7
So,
15a + 5b is divisible by 7
If we substract 14a from above sum still it will remain divisibly by 7 as explained in step 1.
So,
a + 5b is divisible by 7
Now even if we substract some multiple of 7 from above number it will still be divisible by 7.
So, lets substract 7b from above equation we get ,
a + 5b -7b = a-2b
So ( a – 2b ) is divisible by “7”
Hence the proof.
