Question

The sum of a two digit number and the number obtained by reversing the digits is 66. If the digits of the number differ by two, find the number

Answer 1

this is your answer....Thank you ☺️

Answer 2

Answer:

The two numbers that can be formed are 42 and 24.

Step-by-step explanation:

Let the ten's and unit's digit of the number be x and y. So the first number will be 10x + y. Now when the digits are reversed, x becomes the units digit and y the tens digit. So it will be 10y + x.

ATP :

(10x + y) = (10y + x) = 66

11(x + y) = 66x

x + y = 6 -- (I)

The digits differ by 2 :

x - y = 2 -- (I)

y - x = 2 -- (III)

Case 1 :- (I) and (II) :

x + y = 2

x - y = 6

∴ x = 4

Now :

x + y = 6

4 + y = 6

∴ y = 2

Number = 10(x + y)

∴ Number = 42

Case 2 :- (I) and (III) :

x + y = 6

y - x = 2

Now :

x = 6 - y

y - (6 - y) = 2

2y = 8

∴ y = 4

Now :

x + y = 6

x + 4 = 6

∴ x = 2

Number = 10(x + y)

∴ Number = 24

Hence, the two numbers that can be formed are 42 and 24.