Question

3. The sum of the digits of a two digit number is 14. If the number formed by reversing the digits is less
than the original number by 18. Find the original numbers.​

Answer 1

Given :-

• The sum of the digits of a two digit number is 14. If the number formed by reversing the digits is less than the original number by 18.

To find :-

• Original number

Solution :-

Let the tens digit be x then ones digit be y

• Original number = 10x + y

Sum of two digit number is 14

• x + y = 14

Number formed by reversing the digits is less than the original number by 18.

• Reversed number = 10y + x

→ 10x + y - 18 = 10y + x

→ 10x - x + y - 10y = 18

→ 9x - 9y = 18

→ 9(x - y) = 18

→ (x - y) = 18/9

→ (x - y) = 2

Add both the equations

→ (x + y) + (x - y) = 14 + 2

→ x + y + x - y = 16

→ 2x = 16

→ x = 16/2

→ x = 8

Put the value of x in equation (ii)

→ (x - y) = 2

→ 8 - y = 2

→ y = 8 - 2

→ y = 6

Hence,

• Original number = 10x + y = 86
• Reversed number = 10y + x = 68