Question

Show that 954 - 459 is exactly divisible by 99.

Answer 1

$954-459\text{is exactly divisible by}99,wherea=9,b=5,c=4\therefore abc=100a+10b+c\Rightarrow 954=100\times 9+10\times 5+4\Rightarrow 954=900+50+4...\left(i\right)and459=100\times 4+10\times 5+9\Rightarrow 459=400+50+9...\left(ii\right)\text{Subtracting (ii) from (i), we get}954-459=900+50+4-400-50-9\Rightarrow 954-459=500-5\Rightarrow 954-459=495\Rightarrow 954-459=99\times 5Hence,954-459\text{is exactly divisible by 99}\text{Hence proved.}$