question_answer

A three digit number 2 a 3 is added to the number 326 to give a three digit number 5b 9 which is divisible by 9. Find the value of \[b\text{ }-\text{ }a.\]

Answer:

Given,

\[\begin{align}   & \,\,\,\,\,\,2\,\,\,\,a\,\,\,\,3 \\  & \underline{+\,\,\,3\,\,\,\,\,2\,\,\,\,6} \\  & \,\underline{\,\,\,\,5\,\,\,\,\,b\,\,\,\,9} \\ \end{align}\]

Since, 5 b 9 is divisible by 9.

So, (5 + b + 9) is divisible by 9.                                                                                                              ½

So, clearly                             b = 4

and \[\left( 549-326\text{ }=223 \right)\]so,      a =2

Thus,                \[b-a\text{ }=4-2~~\]

=2