Question

Question 89

Solve the following:

Sum of the digits of a two-digit number is 11. The given number is less than the number obtained by interchanging the digits by 9. Find the number.

Answer 1

Let the unit's digit be x. Then, the ten's digit =11-x
$\therefore Number=10(11-x)+x=110-10x+x=110-9x$
Number obtained by interchanging the digits =10x+(11-x)=9x+11
According to the question,
9x+11-(110-9x)=9
$\Rightarrow 9x+11-110+9x=9\Rightarrow 18x=9-11+110\Rightarrow 18x=108\Rightarrow x=\frac{108}{18}\Rightarrow x=6$
Hence, unit's digit=6 and ten's digit=11-6=5
Therefore, the required number is 56.