Question

the sum of two digit no and the no formed by interchanging thier digit is 110. if 10 is subtracted from the first no ,the new no is 4,more than 5 times the sum of the digit in the first no. find the first no.

Answer 1

let the number be xy
$10x + y + 10y + x = 110 \\ 11x + 11y = 110 \\ x + y = 10 \: \: \: \: eq1$
$10x + y - 10 = 5(x + y) + 4 \\ 10x - 5x + y - 5y = 14 \\ 5x - 4y = 14 \: \: \: \: \: eq2 \\ multiply \: eq \: 1 \: by \: 4 \: and \: add \: both \: of \: them \\ 4x + 4y = 40 \\ 5x - 4y = 14 \\ 9x = 54 \\ x = 6 \\ x + y = 10 \\ 6 + y = 10 \\ y = 10 - 6 \\ y = 4 \\ so \: the \: number \: is \: 64$