Question

Sum of a two digit number and the number obtained by reversing the digits is 110 . If 10 is subtracted from the first number , the new number is 4 more than 5 times the sum of the digits in the first number. Find the first number.

Answer 1

Let the 2-digit no. be 10x + y, then
10x + y +10y + x = 110
⇒11x + 11y = 110
⇒x + y = 10
⇒x = 10 - y                      ..............(i)

Now,
10x + y - 10 = 5(x + y) + 4
⇒ 10x + y = 5x + 5y + 14
⇒ 5x - 4y = 14                  .............(ii)

Substituting (i) in (ii), we get
50 - 5y - 4y = 14
⇒ -9y = -36
⇒ y = 4
∴ x = 6
2-digit no. is 6x + y = 60 +4 = 64

Answer 2

Answer:

64

Step-by-step explanation:

Let the 2-digit no. be $10x + y$

Now we are given that Sum of a two digit number and the number obtained by reversing the digits is 110 .

$10x + y +10y + x = 110$

⇒$11x + 11y = 110$

⇒$x + y = 10$

⇒$x = 10 - y$                      ..............(i)

Now we are given that If 10 is subtracted from the first number , the new number is 4 more than 5 times the sum of the digits in the first number.

$10x + y - 10 = 5(x + y) + 4$

⇒ $10x + y = 5x + 5y + 14$

⇒ $5x - 4y = 14$               .............(ii)

Substituting (i) in (ii), we get

$50 - 5y - 4y = 14$

⇒ $-9y = -36$

⇒$y = 4$

So, x = 10-y = 10-4 =6

Thus 2-digit no. is $6x + y = 60 +4 = 64$

Hence the number is 64