Question

A number consists of 2 digits whose sum is 4, if 18 is added ti the number, the digits get interchanged. Then the number is 13

Answer 1

This is not a question. Already answer is indicated in question.

This is to clarify how to get that 13 if not given.

Lets consider the number is

XY ------ [1]

Adding 18 to XY becomes YX

XY + 18 = YX ------- [2]

Split the numbers to tenths and ones (only two digits)

XY = 10X + Y   --------- [3]

YX = 10Y + X ----------- [4]

Apply [3] & [4] in [2]

10X + Y + 18 = 10Y + X

Simplifying further

9X + 18 = 9Y

Divide by 9 both side

X + 2 = Y

X - Y = -2 --------- [5]

Given that

X + Y = 4 ------- [6]

Add [5] and [6]

2X = 2

X = 2/2

X = 1

Apply X =1 in [6]

1 + Y = 4

Y = 4 - 1

Y = 3

So the digit is

13   (XY)

Sum

1 + 3 = 4

If we add 18

13 + 18 = 31

31    (YX)