Question

Sum of the two digit no. is 11.If we interchange the digits it is found that the resulting no. is less than the original no. by 9.What is the two digit no. ​

Answer 1

$\huge\bold\red{ANSWER }$

$\rule{300}{2}$

Let x be the unit digit number

then tens digit number = 11 - x

_____________________________

Since sum of the digits of a two digit

number is 11. ⠀⠀⠀ ⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀

_____________________________

♀ Two digit number (Original) = 10(11-x)+x

= 110 - 10x + x

= 110 - 9x

$\rule{300}{2}$

The two digit number formed by interchanging the digits = 10x + (11 - x)

= 10x + 11 - x

= 9x + 11

$\rule{300}{2}$

According to the condition in the question,

9x + 11 - (110 - 9x) = 9

9x + 11 - 110 + 9x = 9

18x - 99 = 9

18x = 9 + 99 = 108

x = 6

$\rule{300}{2}$

Therefore the required two digit number is = 110 - 9x

= 110 - (9×6)

= 110 - 54

= 56

So the two digit number is $\bold\green{56}$

$\rule{300}{2}$