Question

the sum of the digits of a2-digit number is8 obtained by interchanging the digits exceeds the given number by 18 find the given numbers​

Answer 1

Step-by-step explanation:

The sum of the digits of a 2 digit number is 8.

Let the digits at 1s place be x. Then, the digits at 10s place is (8 - x)

Therefore original number = 10 (8 - x) + x

80 - 10x + x

80 - 9x

On interchanging the digits from 1s to 10s and vice versa

New number obtained = 10x + 8 - x

= 9x + 8

According to the statement, the number obtained by interchanging the digits exceed the original number by 18. The number to find out.

New number - Original number = 18

9x + 8 - (80 - 9x) = 18

9x + 8 - 80 + 9x = 18

18x - 72 = 18

18x = 18 + 72

18x = 90

x = 90 / 18

x = 5

Hence, the digit at 1s place is 5.

Now, digits at 10s place = (8 - 5) = 3.

Thus, the original number is 35 and the new number after interchanging the places of digits is 53.

Answer the original number is 35 and the new number is 53.

"I hope I help you "

Answer 2

Answer:

The number is 35

Step-by-step explanation:

Let,

Units digit = x

Tens digit = 8 - x

★ Original number :

⇒ 10 (8 - x) + x

⇒ 80 - 10x + x

⇒ 80 - 9x

Interchanging the digits exceeds the given number by 18

★ Interchanged digits :

⇒ 10x + 8 - x

⇒ 10x - x + 8

⇒ 9x + 8

★ According to the question :

⇒ 80 - 9x + 18 = 9x + 8

⇒ 80 + 18 - 9x = 9x + 8

⇒ 98 - 9x = 9x + 8

⇒ - 9x - 9x = 8 - 98

⇒ - 18x = - 90

⇒ 18x = 90

⇒ x = 90 / 18

⇒ x = 5

Units digit = 5

Tens digit = 8 - x

⇒ 8 - 5

⇒ 3

Therefore,

The number is 35