Question

sum of the digit of a two digit number is 7 when we interchange the digit it is found that the resulting new number is greater than the original number by 27 what is the two digit number

Answer 1

Okay so let the 2 number be x and y,

Then x+y=7

The original number will be (10x+y) as y is in unit's place and x is in ten's place after reversing we will get (10y+x)

so (10x+y) - (10y+x)=27

Solving it, 10x-x-10y-y=27

9x-9y=27

9(x-y)=27

x-y=3 (dividing by 9 on both side)

So we get 2 equations

x+y=7 and x-y=3

By solving them,

x + y = 7

- x + y = -3

We get 2y=4, so y =2

Putting the value of y in any equation we get x=5.

Hope this helps