Question

the sun of a two digit number and the number obtained by reversing the digit is 66 .if the digit of number differ by 2,find the number.How many such numbers are there​

Answer 1

$Answer:Number is 42.</p><p></p><p>Solution:</p><p></p><p>Let the two digits number is xy,this can be represented as 10x+y</p><p></p><p>on reversing the number the number become yx, now this can be represented as 10y+x</p><p></p><p>according to the question the sum of two digit number and the number reversing the digits is equal to 66</p><p></p><p>\begin{lgathered}10x + y + 10y + x = 66 \\ \\ 11x + 11y = 66 \\ \\ x + y = 6....eq1 \\ \\\end{lgathered}10x+y+10y+x=6611x+11y=66x+y=6....eq1 </p><p></p><p>the digit of the number differ by 2,hence it can be represented algebraically</p><p></p><p>\begin{lgathered}x - y = 2.....eq2 \\ \\\end{lgathered}x−y=2.....eq2 </p><p>Now solve these two equations,here I am using Elimination method,add both equations</p><p></p><p>\begin{lgathered}x + y = 6 \\ x - y = 2 \\ - - - - - - - \\ 2x = 8\\ \\ x = 4 \\ \\4+ y = 6 \\\\y=2\\\\\end{lgathered}x+y=6x−y=2−−−−−−−2x=8x=44+y=6y=2 </p><p></p><p>Hence number is 42.</p><p>it's reverse number is 24.</p><p></p><p>Verification:</p><p>42+24=66</p><p>$