Question

$hey$



The sum of two -digit number and the number obtained by reversing the digits is 66. if the digits of the number differ by 2 , find the number .How many such number are there?​

Answer 1

Answer:

24 or 42

Step-by-step explanation:

Define the number:

Let the digit in the ones place be x.

And the digit in the tens place be y.

The number is (10y + x).

The sum of the two digit number and its reverse is 66.

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

10y + x + 10x + y = 66

11x + 11y = 66

x + y = 6

(Assumption 1) Assuming that x is the larger digit:

The two digits differ by 2.

x - y = 2

x = 2 + y

Sub (x = 2 + y) into (x + y = 6)

(2 + y)  + y = 6

2 + y + y = 6

2 + 2y = 6

2y = 4

y = 2

Sub (y = 2)) into (x = 2 + y):

x = 2 + 2

x = 4

Number = (10x2) + 4 = 24

(Assumption 2): Assumed that y is larger digit:

The two digits differ by 2.

y - x = 2

y = 2 + x

Sub (y = 2 + x) into (x + y = 6)

x + 2 + x = 6

2x + 2 = 6

2x = 4

x = 2

Sub (x = 2) into (y = 2 + x):

y = 2 + 2 = 4

number = (10x4) + 2 = 42

Answer: The number is either 24 or 42.

Answer 2

Answer:

$\underline{\bold{24 \:or\: 42}}$

Step-by-step explanation:

Let the digit in the ones place be x.

And the digit in the tens place be y.

The number is $(10y + x)$.

The sum of the two digit number and its reverse is 66.

$(10y + x) + (10x + y) = 66\\10y + x + 10x + y = 66\\11x + 11y = 66\\x + y = 6$

(Assumption 1) Assuming that x is the larger digit:

The two digits differ by 2.

$x - y = 2\\x = 2 + y$

Substituting $(x = 2 + y)$ into $(x + y = 6)$

$(2 + y)  + y = 6\\2 + y + y = 6\\2 + 2y = 6\\2y = 4\\y = 2$

Substituting $(y = 2)$ into $(x = 2 + y)$:

$x = 2 + 2 \\x = 4$

Number = $(10*2) + 4 = 24$

(Assumption 2): Assumed that y is larger digit:

The two digits differ by 2.

$y - x = 2\\y = 2 + x$

Substituting $(y = 2 + x)$ into $(x + y = 6)$

$x + 2 + x = 6\\2x + 2 = 6\\2x = 4\\x = 2$

Substituting $(x = 2)$ into $(y = 2 + x)$:

$y = 2 + 2 = 4$

Number = $(10*4) + 2 = 42$

The number is either $24$ or $42$.

There are 2 numbers(24 & 42).