Question

25. Sum of the digit 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

$\large\underline{\sf{Solution-}}$

Given that, sum of the digits of a two digit number is 9.

So, Let assume that

• Digit at ones place = x

• Digit at tens place = 9 - x

So, Two digit number or (original number) formed is

$\rm \: = \: x \times 1 + 10 \times (9 - x)$

$\rm \: = \: x + 90 - 10x$

$\rm \: = \:90 - 9x$

Now, number formed by reversing the digits is

$\rm \: = \: 10 \times x + 1 \times (9 - x)$

$\rm \: = \: 10x + 9 - x$

$\rm \: = \: 9 + 9x$

Now, According to statement,

When we interchange the digits, it is found that the resulting new number is greater than the original number by 27.

So, Reverse number = 27 + Original number

$\rm \: 9x + 9 = 27 + 90 - 9x$

$\rm \: 9x + 9 = 117 - 9x$

$\rm \: 9x + 9x = 117 - 9$

$\rm \: 18x = 108$

$\rm\implies \:x = 6$

So,

• Two digit number = 90 - 9 × 6 = 90 - 54 = 36

$\rule{190pt}{2pt}$