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

Answer: The number is 12.

Step-by-step 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,

$14x=-9x+136\\\\14x+9x=136\\\\23x=136\\\\x=\dfrac{136}{23}=12$

So, the number would be

$-9x+120=-9\times 12+120=-108+120=12$

Hence, the number is 12.