Question

The sum of the digits of a two-digit number is 12. If the digits are reversed, the new number
is 12 less than twice the original number. Find the original number​

Answer 1

Answer:

The original number is 48.

Step-by-step explanation:

Given :-

• The sum of the digits of a two-digit number is 12.
• If the digits are reversed, the new number is 12 less than twice the original number.

To find :-

• The original number.

Solution :-

Let the ten's digit of the number be x and the unit's digit of the number be y.

Then,

• The number = 10x+y

According to the 1st condition,

x + y = 12

→ x = 12-y..............(i)

According to the 2nd condition,

10y+x = 2(10x+y) - 12

→ 10y + 12-y = 20x+2y - 12

→ 10y + 12-y = 20(12-y) + 2y - 12

→ 10y + 12-y = 240 - 20y + 2y -12

→ 10y-y+20y-2y = 240-12-12

→ 27y = 216

→ y = 8

Now put y=8 in eq(i)

x = 12-y

→ x = 12-8

→ x = 4

Therefore,

• The original number = 10×4+8 = 48

Answer 2

Let, the tens digit number be x

the ones digit number be 12-x

Original number = {10x+(12-x)}

After interchanging the digits, the new number

= {10(12-x)+x}

ATP

{10(12-x)+x} = 2{10x+(12-x)} - 12

=) 120-10x+x = 2(10x+12-x) - 12

=) 120-10x+x = 20x+24-2x-12

=) 120+12-24 = 20x+10x-2x-x

=) 132-24 = 30x-3x

=) 108 = 27x

=) 108/27 = x

=) 4 = x

Ans:- The Original number = {10x+(12-x)}

• = {(10×4)+(12-4)}
• = (40+8)
• = 48