Question

A number consists of two digits whose sum is 12. If 16 is added to the number, then one of the digits is four times the value of the other. What is the number?

Answer 1

66

Explanation:

Brute force:

2 digit numbers that has sum of 12:

39, 48, 57, 66

Add 16 to the numbers:

55, 64, 73, 82

Find the number that shows a digit is 4 times the value of other:

82 (2x4 =8)

Answer 2

Answer: The number is 12.

Explanation:

Since we have given that

Sum of two digits = 12

Let the one's digit be 'x'

Let the ten's digit be '12-x'

So, Original number would be

`x+10(12-x)\\\\=x+120-10x\\\\=-9x+120`

If 16 is added to the number, then one of the digit is four times the value of the other.

According to question, we get that

`-9x+120+16\\\\=-9x+136`

so, the one's digit be 'x'.

Let the ten's digit be '4x'.

so, New number would be

`10x+4x=14x`

According to question, it becomes,

`14x=-9x+136\\\\14x+9x=136\\\\23x=136\\\\x=(136)/(23)=12`

So, the number would be

`-9x+120=-9* 12+120=-108+120=12`

Hence, the number is 12.