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 2 find the number​

Answer 1

Answer:Number is 42.

Solution:

Let the two digits number is xy,this can be represented as 10x+y

on reversing the number the number become yx, now this can be represented as 10y+x

according to the question the sum of two digit number and the number reversing the digits is equal to 66

\begin{gathered}10x + y + 10y + x = 66 \\ \\ 11x + 11y = 66 \\ \\ x + y = 6....eq1 \\ \\\end{gathered}

10x+y+10y+x=66

11x+11y=66

x+y=6....eq1

the digit of the number differ by 2,hence it can be represented algebraically

\begin{gathered}x - y = 2.....eq2 \\ \\\end{gathered}

x−y=2.....eq2

Now solve these two equations,here I am using Elimination method,add both equations

\begin{gathered}x + y = 6 \\ x - y = 2 \\ - - - - - - - \\ 2x = 8\\ \\ x = 4 \\ \\4+ y = 6 \\\\y=2\\\\\end{gathered}

x+y=6

x−y=2

−−−−−−−

2x=8

x=4

4+y=6

y=2

Hence number is 42.

it's reverse number is 24.

Verification:

42+24=66

Answer 2

Answer:

$\huge{\boxed{\rm{\pink{Number=42}}}}$

Step-by-step explanation:

Given:-

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 2.

To find:-

find the number

Solution:-

Let the digits in a two digit number be "a" and "b"

"a" is in 10's place

The place value of a =10a

"b" is in 1's place

The place value of b =b

Now the two digit number =10a+b

The number obtained by reversing the digits =10b+a

Condition 1:-

the sum of a two digit number and the number obtained by reversing the digits is 66

=>(10a+b)+(10b+a)=66

=>10a+a+10b+b=66

=>11a+11b=66

=>11(a+b)=66

=>a+b=66/11

=>a+b=6.......(1)

Condition 2:-

the digits of the number differ by 2

=>a-b=2..........(2)

From (1)&(2)

a+b=6

a-b=2

(+)

______

2a+0=8

_______

=>2a=8

=>a=8/2

=>a=4

from(1)

=>4+b=6

=>b=6-4

=b=2

we have a=4 and b=2

number=10a+b=10(4)+2=40+2=42

Answer:-

The required number=42

Check:-

Condition 1:-

42+24=66

Condition 2:-

4-2=2