Question

in a two digit number difference of digits is 5 if that number divided by 2 and 2 added to the answer then original two digit number get reversed what is that number​

Answer 1

Let ,

The unit's digit be " y "

The ten's digit be " x "

The original number be " 10x + y "

Case I

In a two digit number , the difference of digits is 5

x - y = 5 --- (i)

Case II

If a number divided by 2 and 2 added to the answer then original two digit number get reversed

(10x + y)/2 + 2 = 10y + x

(10x + y + 4)/2 = 10y + x

10x + y + 4 = 20y + 2x

8x - 19y = -4 --- (ii)

Multiply eq (i) by 8 , we get

8x - 8y = 40 --- (iii)

Subtract eq (ii) by eq (iii) , we get

8x - 8y -(8x - 19y) = 40 - (-4)

11y = 44

y = 4

Put the value y = 4 in eq (i) , we get

x - 4 = 5

x = 9

$\therefore \underline{\sf{The \: original \: number \: is \: 94}}$