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 ?

Answer 1

Let the digit in units place $=x$

The digit in tens place $=3x$

The number is $10\left(3x\right)+x$---(1)

Digits are interchanged

Digit in units place $=3x$

Digit in tens place $=x$

The new number $=10\left(x\right)+3x$ ---(2)

It is given that, sum of these two numbers $=88$

$\Rightarrow 10\left(3x\right)+x+10\left(x\right)+3x=88$

$\Rightarrow 30x+x+10x+3x=88$

$\Rightarrow 44x=88$

$\Rightarrow x=\frac{88}{44}$

$\Rightarrow x=2$

from (1)

The number $=10\left(3x\right)+x=10(3\times 2)+2=60+2=62$

Therefore, the required numbers are $62$ or $26$