Question

Write all the 2-digit number which when added to 27 get reversed

Answer 1

Step-by-step explanation:

let the unit place and the 2nd place digits are...x and y repectively

now the number is=10y+x

now according to the question if 27 is added the number get reversed....

10y+x+27=10x+y

9y+27=9x

x-y=3

the sum of the digits is=5

x+y=5

solving the equations

x=4

y=1

therefore the number is 14and if 27 is added the number becomes reversed I,e,41

Answer 2

Answer:

Step-by-step explanation:

Let us take the number as xy, where the tens digit is x and ones digit is y.

Thus, 10x+y+27=10y+x

Thus, 10x-x+27=10y-y

9x+27=9y

9(x+3)=9*y

Thus, x+3=y

The limit for a digit of a number is 9

Thus, the numbers that are possible are-

x y

9 6

8 5

7 4

6 3

5 2

4 1

We cannot take x as 3, as if we do, y would be 3-3=0, and the number so obtained after reversing would be 3, which is not a 2-digit number.

Nor can x be 2,1 or 0 as if we subtract 3 from these to find y, we would get a negative number.

Thus, the numbers are:

96, 85, 74, 63, 52 and 41.