Question

The sum of two digits of a 2-digit number is 11. Reversing the digits increase the number by 45. What is the number?​

Answer 1

Answer:

The number is   38

Step-by-step explanation:

Let,

Units digit = y

Tens digit = 11 - y

Original no :

⇒ 10 (11 - y) + y

⇒ 110 - 10y + y

⇒ 110 - 9y

Reversing the digits increase the number by 45 :

⇒ 10y + (11 - y)

⇒ 10y - y + 11

9y + 11

★ According to the  Question :

⇒ (110 - 9y)  + 45  =  9y + 11

⇒ 110 + 45 - 9y   =  9y + 11

⇒ 155 - 9y  =  9y + 11

⇒ - 9y - 9y  =  11 - 155

⇒ - 18y  =  - 144

⇒  18y  =   144

⇒  y  =  144 / 18

⇒  y  =  8

Units digit = 8

Tens digit = 11 - y

⇒ 11 - 8

⇒ 3

∴ The number is   38

Answer 2

Explanation:

A two digit positive integer can be written as 10x+y, where x is the ten's digit and y is the one's digit.

For example, 52 = 10(5)+2

So, if we let x = ten's digit and y = one's digit, then:

x+y=11

(10x+y)+45 = 10y+x

Simplify to get x+y = 11

9x-9y = -45

Dividing the second equation by 9, we have x+y = 11

x -y = -5

Add the equations to obtain 2x = 6. So, x = 3

Since x+y=11 and x=3, y = 8.

The number is 38.