Question

one of the two digits of a two digit number is three times the other digit if you interchange the digits of these two digit number and add the resulting number to the original number you get 88 what is the original number

Answer 1

• Let x be the digit in tens place and y digit in unit's place
• Then, the number is 10x + y.
• Also, The number obtained on reversing the digits is 10y + x.

According to the Question,

10x + y +(10y + x) = 88
=> 11x + 11y = 88
=> 11(x + y) = 88

$\bf{=>\:x\:+\:y\:=\:8}$ _____(1)

Assuming, $\bf{x \:-\:3y\:=\:0}$_____(2)

Subtracting equation (2) from equation (1) we get,

(x-x) + (y -(-3y)) = (8-0)
=> 4y = 8
=> $\bf\large\textit{y = 2}$

Substituting value of y in equation (1) we get,

x + 2 = 8
=>$\bf\large\textit{x\:=\:6}$

Hence, the number is 10(6) + 2.
=> $\bf\huge{62}$