Question

One of the two digits of a two digit number is three times the other digit. If you interchange the digits of this two digit number and add the resulting number to the original number, you get 88. What is the original number?
(a). 88
(b). 26
(c). 62
(d). 68

Answer 1

Hint: First we will take the two digits number as xy and then we will apply the given condition in the question and then we will interchange the two digit number and it becomes yx and then we will add it to get our final answer of 88.

Complete step-by-step solution -

Let the two digit number be xy.
Now as per the given question one of the two digits of a two digit number is three times the other digit.
Therefore,
y = 3x
Now we will break xy in tens and ones,
$xy=10x+y$
Now using y = 3x in the above equation we get our number as,
$\begin{align}
  & 10x+3x \\
 & =13x \\
\end{align}$
Now interchanging the digits of this two digit number we get
$yx=10y+x$
Now using y = 3x in the above equation we get our number as,
$\begin{align}
  & 10(3x)+x \\
 & =31x \\
\end{align}$
Now as per the question,
$\begin{align}
  & 31x+13x=88 \\
 & 44x=88 \\
 & x=\dfrac{88}{44} \\
 & x=2 \\
\end{align}$
Now putting the value of x in y = 3x we get,
y = $3\times 2$ = 6
Now the number that we took was xy and hence 26.
So, option (b) is correct.
And if we would have taken x = 3y then the answer that we get is 62.
So, option (c) is also correct.

Note: One thing in this question should be kept in mind that there are two answers to this question, so one might think after solving that only one answer is correct and can make mistakes so this should be kept in mind.