Question

Question 3
Sum of the digits of a two-digit number is 9. When we interchange the digits, it is found that the resulting new number is greater than the original number by 27. What is the two-digit number?

Answer 1

Let the unit place digit of a two-digit number bex.
Therefore,the tens place digit =9 - x
$\because$ 2-digit number = 10 $\times$ tens place digit + unit place digit
Original number = 10(9 - x)+x

According to the question,
New number = Original number +27
$\Rightarrow 10x+(9-x)=10(9-x)+x+27$
$\Rightarrow 9x+9=90-10x+x+27$
$\Rightarrow 9x+9x=117-9$
$\Rightarrow 18x=108$
$\Rightarrow x=\frac{108}{18}=6$

Hence,the 2-digit number
$=10(9-x)+x$
$=10(9-6)+6$
$=10\times 3+6$
$=30+6$
$=36$