Reversed Intergers

[cherire]

Q.
How many intergers n greater than 10 and less than 100 are there such that, if the digits of n are reversed, the resulting inter is n+9?
a. 5
b. 6
c. 7
d. 8
e. 9

Can you please explain your answers in detail. Thanks!

[chix475ntu]

let the number be ab where 'a' is the tens digit and 'b' units digit
so the number = 10a + b
reverse it = 10b+a

given than 10a + b + 9 = 10b+a
==> 9a+9=9b ==> a+1 = b

so there will be 8 numbers (12, 23,34,45,56,67,78,89)

D

[cherire]

Thanks a lot.