Answer:
The smaller of the consecutive number is 36
Explanation:
Let the digits be ab, and ab + 1, therefore, we are given;
The given parameters are;
ab
+ ab + 1
b+1 a
Therefore, we note that adding the two unit numbers b and b + 1, will give a number larger than 10, from which we carry the number 1 on the tens side to be added to the tens unit of when adding the tens unit side of the two numbers as follows;
b + b + 1 = 10 + a...(1)
1 + a + a = b + 1...(2)
From equation (2), we have;
1 + a + a = b + 1
b + 1 = 1 + a + a
b = 2·a...(3)
Substituting the value of b from equation (3) in equation (1) gives;
b + b + 1 = 10 + a
2·a + 2·a + 1 = 10 + a
4·a - a = 10 - 1
3·a = 9
a = 9/3 = 3
a = 3
From equation (3) b = 2·a = 2 × 3 = 6
b = 6
The numbers are a b, and a b + 1 which are 36 and 36 + 1 = 37
We check to get;
36 + 37 = 73
Arranging 73 in reverse order = 37 which is the largest of the consecutive numbers
Therefore, the smaller of the consecutive number = 36.