Question

One of the two digits of a 2-digit number is 3 times the other digit. If you interchange the digits of this 2-digit number and add the resulting number to the original number, you get 88. What is the original number?

Answer 1

Hint: Let us take the unit digit of the original number to be ‘x’. Follow the data provided in the question statement to form the necessary equations.

Complete step-by-step answer:
As the unit’s digit of the original number is ‘x’, then, digit in the ten's place will be ‘3x’.
So, the original number will be

\[10\left( 3x \right)\text{ }+\text{ }x\text{ }=\text{ }31x\]

On interchanging the digits, the new number so formed will be

\[10x\text{ }+\text{ }3x\text{ }=\text{ }13x\]

According to the question, on adding the original number with the number formed after interchanging the digits, the sum will be 88.

So,

\[\begin{array}{*{35}{l}}
   \left\{ 10\left( 3x \right)\text{ }+\text{ }x \right\}\text{ }+\text{ }\left\{ \text{ }10x\text{ }+3x \right\}\text{ }=\text{ }88 \\
   ~ \\
   31x\text{ }+\text{ }13x\text{ }=\text{ }88 \\
   ~ \\
   44x\text{ }=\text{ }88 \\
   ~ \\
   x\text{ }=\text{ }2 \\
\end{array}\]

Therefore, the original number will be:-
 10(3x2) + 2 = 31x2=62

And the number obtained after reversing the digits will be
10x2 + 3x2 = 13x2 =26

Note: Read the questions very carefully as there are very minute details in the question. Skipping any single detail can lead the student into the wrong direction. The entire question has information that is essential and missing out on any of these details could be costly later as the question unfolds.