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