Question

The sum of digits of a number is 12. If both are interchanged, then the newly formed number is 36, more than the original number. What is the original number?​

Answer 1

Answer:

$\huge \orange{48}$

Step-by-step explanation:

First you need to know that in our decimal system if a number is written as [ab] then the value of that number is 10a + b . For example if a number is 56 then 56 = 10 × 5 + 6 .

Now let unit digit of number be x then other digit of our original number will be 12 - x ( because sum of both are is 12 given ) .

So our original number will be

$= 10(12 - x) + x \\ = 120 - 10x + x \\ = 120 - 9x \: \: \: \: \: \: \: \: \: \:$

Now when we flip the digits new number formed will be

$10(x) + (12 - x) \\ = 10x + 12 - x \\ = 9x + 12 \: \: \: \: \: \: \: \: \: \:$

Now also given that this new number is 36 more then original one so

$9x + 12 = (120 - 9x) + 36 \\ \\ \implies \: 9x + 12 = 156 - 9x \\ \\ \implies 9x + 9x = 156 - 12 \\ \\ \implies 18x = 144 \\ \\\implies x = \frac{144}{18} = 8$

And other digit will be

$= 12 - 8 = 4$

So number formed is 48 .