Question

There are certain 2-digit numbers.The difference between the number and the one obtained on reversing it is always 27.How many such maximum 2-digit numbers are there? 

(a) 3 

(b) 4 

(c) 5 

(d) None of the above

Answer 1

Correct option (d) None of the above

Explanation:

Let the numbers be of the form xy and yx, i.e. 10x + y and 10y + x (where y > x)

As per the question, (10y + x) – (10x + y) = 27

Or 9y – 9x = 27

Or y – x = 3

Or y = x + 3

So, possible sets of the value of x and y are: (1, 4), (2, 5), (3, 6), (4, 7), (5, 8) and (6, 9), i.e. 6 such numbers are there.