Question

The tens And units digit of a two digit number differ by one .if the digits are reversed and the new number obtained is added to the original number the result is 99 the original number is​

Answer 1

Answer:

If the difference between tens and units digit of a two-digit number is 1 and if the number is reversed and added to the original number, then the sum is 99, then the number is 54

Step-by-step explanation:

Let XY be the two-digit number

Given the tens and unit digits of XY differ by one

That is, X-Y=1

If XY is reversed it becomes YX

Given XY+YX=99

As XY is a two-digit number,

10X+Y +10Y+X=99

11X+11Y=99

X+Y=99/11 =9

X+Y=9

X-Y=1

X=Y+1

So X+Y =Y+1+Y = 2Y+1

So 2Y+1 = 9

2Y= 8

Y= 8/2 =4

So X = Y+1 =5

So the two-digit number is 54