Question

4 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

$\large\underline{\sf{Solution-}}$

Given that,

One of the two digits of a two digit number is three times the other digit.

So, 2 cases arises

Case :- 1

Let assume that digit at units place be x

So, digit at tens place be 3x.

Original number formed = 1 × x + 10 × 3x = x + 30x = 31x

Reverse number = 10 × x + 1 × 3x = 10x + 3x = 13x

Further given that,

If we interchange the digits of this two-digit number and add the resulting number to the original number, we get 88.

$\rm \: 31x + 13x = 88$

$\rm \: 44x = 88$

$\rm\implies \:x = 2$

So, Original two digit number = 31 × 2 = 62

Case :- 2

Let assume that digit at tens place be x

So, digit at ones place be 3x.

Original number formed = 10 × x + 1 × 3x = 10x + x = 13x

Reverse number = 1 × x + 10 × 3x = x + 30x = 31x

Further given that,

If we interchange the digits of this two-digit number and add the resulting number to the original number, we get 88.

$\rm \: 13x + 31x = 88$

$\rm \: 44x = 88$

$\rm\implies \:x = 2$

So, original two digit number is 26.