Question

the difference between a two digit number and the number obtained by interchanging the digits is 36. which of the following could not be the sum of the digits of the number?

a)6 b)8 c)9 d) 12 e) 14

Answer 1

Let the number in the tenth's digit be x and the number in one's digit be y. The number thus obtained = 10x + y
On reversing the digits we get : 10y + x

Now, according to the question, we have
(10x + y) - (10y + x) = 36
= 10x - x + y - 10y = 36
= 9x - 9y = 36
= x - y = 4
= x = 4 + y ............ (i)

Next we check the values of the options and check which statement is false.
a) We apply x + y = 6 (x + y is the sum of the digits)
Substituting value of x from (i), we get  :
(4 + y) + y = 6
= 4 + 2y = 6
= 2y = 2
= y = 1 (The value of y can be 1 so the statement is true)

b) We apply x + y = 8
Substituting value of x from (i), we get  :
(4 + y) + y = 8
= 4 + 2y = 8
= 2y = 4
= y = 2 (The value of y can be 2 so this statement is also true)

c) We apply the value x + y = 9
Substituting value of x from (i), we get  :
(4 + y) + y = 9
= 4 + 2y = 9
= 2y = 5
= y = 5/2 (The value of y can never be a fraction so the statement is false)
Therefore the answer is option c) 9

Hope that helps !!