Question

3 The sum of the digits of a 2-digit number is 8. The number obtained by
interchanging the digits exceeds the given number by 18. Find the given numbers.​

Answer 1

Given :

• The sum of the digits of 2-digit number is 8.
• By interchanging the digits exeeds the given number by 18.

To find :

• The given number.

Solution :

Let the digit at ones place be x

Then the digit at tens place will be 8 - x

[Because it is given that sum of two numbers is 8]

Thus, the original number will be :

• 10 × (8 - x) + x
• 80 - 10x + x
• 80 - 9x

Now, on interchanging the digits of the given number.

The ones place will be 8 - x

And tens place will be x

So,New number will be :

• 10 × (x) + 8 - x
• 10x + 8 - x
• 10x - x + 8
• 9x + 8

It is given that the new number exceeds the original number by 18.

Therefore,

New number - Original number = 18

A/Q

↬ (9x + 8) - (80 - 9x) = 18

↬ 9x + 8 - 80 + 9x = 18

↬ 9x + 9x - 72 = 18

↬ 18x = 18 + 72

↬ 18x = 90

↬ x = 90/18

↬ x = 5

∴ The digit at ones place = x = 5

And digit at tens place = 8 - x = 8-5 = 3

Thus,

• The original number = 35

Verification :

→ Sum of digit in original number = 8 (given)

→ 3 + 5 = 8

On interchanging the digits, the new number is 53.

So,

New number - original number = 18

→ 53 - 35 = 18

→ 18 = 18

Hence, Solution is verified !

Answer 2

Step-by-step explanation:

Let the digits at ones place be x. Then,

the digits at tens place = (8-x)

Original number = 10(8-x) + x

= 80 - 10x + x

= 80 - 9x

On interchanging the digits

new number obtained = 10x + 8-x

= 9x + 8

According to question,

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 digits at ones place is 5.

The digits at tens place = (8-5) = 3.

So, the original number is 35 and the new number is 53.