Question

The sum of the digits of a 2 digit no is 11.If the digits are reversed then the no increases by 27. Find the no

Answer 1

Answer:

step by step explanation:

Answer 2

$\setlength{\unitlength}{1.0 cm}}\begin{picture}(12,4)\linethickness{3mm}\put(1,1){\line(1,0){6.8}}\end{picture}$

$\underline{\blacksquare\:\:\:\footnotesize{\red{\text{SolutioN:-}}}}$

$\footnotesize{\text{let , the 2 digits are x and y at the at the unit and}}$

$\footnotesize{\text{2'nd place}}$

$\footnotesize{\therefore\:\:\text{The original number is = 10y+x}}$

$\footnotesize{\therefore\:\:\text{The reverse number is = 10x+y}}$

$\footnotesize{\underline{\text{According to condition 1 , }}}$

$\footnotesize{\therefore\:\:x+y=11 \:\:}$

$\footnotesize{\therefore\:\:y=11-x\: \:--------(1)}$

$\setlength{\unitlength}{1.0 cm}}\begin{picture}(12,4)\linethickness{1mm}\put(1,1){\line(1,0){6.8}}\end{picture}$

$\footnotesize{\underline{\text{According to condition 2 , }}}$

$\footnotesize{\red{\text{reversed number-original number=27}}}$

$\footnotesize{10x+y-(10y+x)=27}$

$\footnotesize{10x+y-10y-x=27}$

$\footnotesize{9x-9y=27}$

$\footnotesize{9(x-y)=27}$

$\footnotesize{(x-y)=\dfrac{\cancel{27}}{\cancel{9}}}$

$\footnotesize{x-y=3}$

$\footnotesize{x=3+y}$

$\footnotesize{x=3+11-x\:\:\:\:\:\text{(from equation (1) , )}}$

$\footnotesize{x+x=14}$

$\footnotesize{2x=14}$

$\footnotesize{x=\dfrac{\cancel{14}}{\cancel2}}$

$\footnotesize{\red{x=7}}$

$\footnotesize{\text{putting x=7 in equation (1) , )}}$

$\footnotesize{y=11-7}$

$\footnotesize{\red{y=4}}$

$\footnotesize{\red{\therefore\:\text{the original number is = 10(4)+7=47}}}$

$\setlength{\unitlength}{1.0 cm}}\begin{picture}(12,4)\linethickness{3mm}\put(1,1){\line(1,0){6.8}}\end{picture}$