Question

The sum of the digits of two digit
number is 8. The number obtained by
interchanging the digit exceeds the given
number by 18. Find the given number.​

Answer 1

Answer:

35

Step-by-step explanation:

Given :

The sum of the digits of two digit number is 8.

The number obtained by interchanging the digit exceeds the given

number by 18.

Find the given number.​

Solution :

Let the digits be x y

i.e., = 10x + y,.

Statement 1 :

The sum of the digits of two digit number is 8.

⇒ x + y = 8 ...(i)

Statement 2 :

The number obtained by interchanging the digit exceeds the given

number by 18.

Original number = 10x + y

When the digits gets interchnged,

It will be , 10y + x,.

It exceeds by 18

⇒ (10y + x) = (10x + y) + 18

⇒ (10y + x) - (10x + y) = 18

⇒ 10y + x - 10x - y = 18

⇒ 10y - y + x - 10x = 18

⇒ 9y - 9x = 18

⇒ 9 × (y - x) = 9 × 2

⇒ y - x = 2

By multiplying both the sides , by (-1),

We get,

⇒ -1 × (y - x) = -1 × (2)

⇒ - y + x = -2

⇒ x - y = -2 ...(ii)

By adding (i) & (ii),

We get,

⇒ (i) + (ii)

⇒ (x + y) + (x - y) = 8 + (-2)

⇒ x + x + y - y = 8 - 2

⇒ 2x = 6

⇒ x = 3,.

By substituting the value of x, in (i),

⇒ x + y = 8

⇒ 3 + y = 8

⇒ y = 8 - 3

⇒ y = 5,.

The given number is 10x + y = 3 × 10 +  = 30 + 5 = 35