Question

the sum of digits of two digit number is 11 when the digits are interchanged the new number formed is less than original number by 27 find the original number​

Answer 1

$\large\underline{\underline \red{\bigstar{\textbf{\textsf{\: question\::-}}}}}$

sum of digit of a two digit number is 11 when the digit are interchanged the new number formed is less than the original number by 27 find the original number

$\large\underline{\underline \red{\bigstar{\textbf{\textsf{\: given\::-}}}}}$

sum of digit of a two digit number is 11 when the digit are interchanged the new number formed is less than the original number by 27.

$\large\underline{\underline \red{\bigstar{\textbf{\textsf{\: to \: find\::-}}}}}$

the original number

$\large\underline{\underline \red{\bigstar{\textbf{\textsf{\: solution\::-}}}}}$

let the number be 10x + y

And the other number when digit are interchanged be 10y + x

$\sf⇝ sum \: of \: digit \: = 11$

$\sf⇝ x + y = 11$

$\sf⇝ y - 11 - x - - - - (1)equation$

new no is 2 times less than original number

$\sf⇝ (10x + y) - 27 = 10y + x$

$\sf⇝ 10x - x - 27 = 10y - y$

$\sf⇝ 9x - 27 = y$

$\sf⇝ x - 3 = y - - - - - (2)equation$

now (1) in (2) we get

$\sf⇝ x - 3 = 11 - x$

$\sf⇝ 2x = 14$

$\sf⇝ x = \frac{14}{2}$

$\sf⇝ x = \cancel\frac{14}{2}$

$\sf⇝ x = 7$

X = 7 in (2) we get

$\sf⇝ 7 - 3 = y$

$\sf⇝ y = 4$

original number = 10x + y

= 10(7) + y

= 74

so therefore the original number is 74 or 47