Question

the sum of a num of two digits and of the num formed by reversing the digit is 110 and the difference of the digit is 6. find the number​

Answer 1

$\tt \: Let \: digit \: at \: unit \: place \: be \: x \\ \tt \: and \\ \tt \: Let \: digit \: at \: tens \: place \: be \: y$

$\tt \: So, \: number \: formed \: = 10y + x \\ \tt \: and \\ \tt \: Reverse \: number \: = \: 10x + y \: \: \: \: \: \: \:$

$\tt \: \begin{gathered}\bf\red{ \tt \:1. \: According \: to \: statement}\end{gathered}$

$\tt \:  ⟼\tt \: 10y + x + 10x + y = 110$

$\tt \:  ⟼ \tt \: 11x + 11y = 110$

$\tt\implies \:x \: + \: y \: = 10 - - - (1)$

$\tt \: \begin{gathered}\bf\red{ \tt \:2. According \: to \: statement}\end{gathered}$

$\tt \: difference \: of \: digits \: of \: number \: = 6$

$\tt\:  ⟼ x \: - y \: = 6 - - - - (2) \\ \tt \: or \\ \tt \:  ⟼y \: - \: x \: = 6 - - - - (3)$

☆ Now, solving equation (1) and equation (2)

$\tt \: On \: adding \: equation \: (1) \: and \: (2) \: we \: get$

$\tt \: \tt \:  ⟼2x \: = 16$

$\tt \:  ⟼ \: x \: = \: 8 \: - - - (4)$

$\tt \: On \: substituting \: x \: = 8 \: in \: equation \: (1) \: we \: get$

$\tt \:  ⟼ \: 8 \: + \: y \: = \: 10$

$\tt \:  ⟼ \: y \: = \: 2$

$\bf\implies \:Hence, \: number \: is \: 10y + x = 10 \times 2 + 8 = 28$

─━─━─━─━─━─━─━─━─━─━─━─━─

☆ Now, solving equation (1) and equation (3)

$\tt \: On \: adding \: equation \: (1) \: and \: (3) \: we \: get$

$\tt \:  ⟼ \: 2y \: = 16$

$\tt \:  ⟼ \: y \: = \: 8 - - - (5)$

$\tt \: On \: substituting \: y \: = 8 \: in \: equation \: (1) \: we \: get$

$\tt \:  ⟼x + 8 \: = 10$

$\tt \:  ⟼ \: x \: = \: 2$

$\bf\implies \:Hence, \: number \: is \: 10y + x = 10 \times 8 + 2 = 82$

─━─━─━─━─━─━─━─━─━─━─━─━─

$\begin{gathered}\begin{gathered}\bf Hence, \: number \: is - \begin{cases} &\tt{28} \\ &\tt{82} \end{cases}\end{gathered}\end{gathered}$