Question

The hundreds digit and the ones digit of a three digit number are the same. The sum of its tree digits are 16. If the tens digit and the ones digit are exchanged, the number increases by 45. What is the number?

Answer 1

727

Step-by-step explanation:

       Let us denote the three digit number by $abc$, where $a$ is the hundreds digit, $b$ is the tens digit and $c$ is the ones digit.

       Hundreds digit = $a$ = Ones digit = $c$

       Sum of digits = $a+b+c=16$

       So, $2c+b=16$

       On exchanging tens and ones digit, value increases by 45. So $acb$ is 45 greater than $abc$.

       $acb-abc=45$

       $100a+10c+b-100a-10b-c=45\\9c-9b=45\\c-b=5$

       $2c+b=16,c-b=5\\3c=21\\c=7=a\\b=2$

∴ Required number is 727