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. How many such numbers are there?​

Answer 1

Solution :

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

on reversing the number thee 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

10x + y + 10y + x = 66

11x + 11y = 66

x + y = 6...........(eq 1)

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

x - y = 2...........(eq2)

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

x + y = 6 + x - y = 2

2x = 8

x = 8/2

x = 4

4 + y = 6

y = 6 - 4

y = 2

Hence number is 42. its reverse number is 24.

Verification:

Here,

42 + 24 = 66

4 - 2 = 2,

Also

24 + 42 = 66

4 - 2 = 2

Answer 2

Answer:

✳️ Given ✳️

$\longmapsto$ 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 ✳️

$\longmapsto$ What is the number.

✳️ Solution ✳️

✒️ Let's assume the digit at unit's place as x and ten's place as y. Then, the number will be 10y + x.

✏️ The two digits of the number are differing by 2.

$\Rightarrow$ x - y = 2 ....... (1)

$\Rightarrow$ x - y = - 2 ...... (2)

✏️ Now after reversing the order of the digits, the number becomes 10x + y.

➕ According to the question,

$\longrightarrow$ (10x + y) + (10y + x) = 66

$\implies$ 10x + y + 10y + x = 66

$\implies$ 11x + 11y = 66

$\implies$ 11(x + y) = 66

$\implies$ x + y = $\sf\dfrac{\cancel{66}}{\cancel{11}}$

$\dashrightarrow$ x + y = 6 ..... (3)

✏️ On adding the equation no (1) and (2) we get,

$\implies$ (x - y) + (x + y) = 2 + 6

$\implies$ x - y + x + y = 8

$\implies$ 2x = 8

$\implies$ x = $\sf\dfrac{\cancel{8}}{\cancel{2}}$

$\dashrightarrow$ x = 4

✏️ Putting the value of x in the equation no (3) get,

$\Rightarrow$ 4 - y = 2

$\implies$ y = 4 - 2

$\dashrightarrow$ y = 2

Hence, the required number is 10 × 2 + 4 = 24

Now,

✏️ On adding the equation no (2) and (3) we get,

$\Rightarrow$ (x - y) + (x + y) = - 2 + 6

$\implies$ x - y + x + y = 4

$\implies$ 2x = 4

$\implies$ x = $\sf\dfrac{\cancel{4}}{\cancel{2}}$

$\dashrightarrow$ x = 2

✏️ Putting the value of x in the equation no (3) we get,

$\Rightarrow$ 2 - y = - 2

$\implies$ y = 2 + 2

$\dashrightarrow$ y = 4

Hence, the required number is 10 × 4 + 2 = 42

$\therefore$ There are two such possible numbers is 24 and 42.

__________________ ⭐ ________________