Question

Show that 954 – 459 is exactly divisible by 99.

Answer 1

To show : 954 – 459 is exactly divisible by 3 99, where a = 9, b = 5, c = 4  abc = 100a + 10b + c 

=> 954 = 100 x 9 + 10 x 5 + 4 

=> 954 = 900 + 50 + 4 ………(i)

and 459 = 100 x 4+ 10 x 5 + 9 

=> 459 = 400 + 50 + 9 ……..(ii)

Subtracting (ii) from (i), we get 

954 – 459 = 900 + 50 + 4 – 400 – 50 – 9

=> 954 – 459 = 500 – 5 

=> 954 – 459 = 495 

=> 954 – 459 = 99 x 5

Hence, 954 – 459 is exactly divisible by 99 

Hence proved.