Question

Sum of the digits of a two digit number is 12. When we interchange the digits, it is found that

the resulting new number is greater than the original number by 18. What is the Original two

digit number?​

Answer 1

Answer:

57     (Please mark me as brainliest!)

Step-by-step explanation:

If the first digit is represented as a and the second is represented as b:

Then the number n = 10a + b and it’s reverse is 10b + a.

The rules are:

a + b = 12

And

(10b + a) - (10a + b) = 18

This simplified is:

10b + a - 10a - b = 18

9b - 9a = 18

We can factor out 9

9(b - a) = 18 and simplify

b - a = 2

b = 2 + a we can use this to solve for a using:

a + b = 12

a + (2 + a) = 12 Simplify

2a + 2 = 12

2a = 10

a = 5 Now we solve for b

b - a = 2

b - (5) = 2

b = 7

So a = 5 and b = 7 and we can find the number n by using the equation we had before:

n = 10a + b

n = 10(5) + 7

n = 50 + 7

n = 57

The answer is 57.