Question

a number consists of two digits whose sum is 6. if 18 is added to the number its digits are reversed. find the number.​

Answer 1

Let the two digit number be xy.

Given x+y=6 and if we add 18 to xy then the number becomes yz.

Here we know that y=6-x.

10x+y+18=10y+x

10x+6-x+18=60-10x+x

18x=36

x=2,y=4.

Thus the two digit number is 24.

Answer 2

let the unit digit be x

and tens digit be y

then, original number will be 10y + x

and reversed number = 10x + y

a/q. x + y = 6...........(1)

and , 10y+x + 18 = 10x +y

10y -y + x-10x = - 18

9y - 9x = -18

9 (y-x) = -18

y-x = -2....... (2)

adding (1) &(2)

x+y + y - x = 6-2

2y = 4

y= 2

putting y =2 in (1)

x+1 = 6

x = 5

so, unit digit = 5 and tens digit= 2

this the original number is 25