Question

sum of the digit of a two digit number is 8 when we interchange the digits it is found that the resulting new number is greater than the original number by 18 what is the two digit number

Answer 1

Given :-

• Sum of the digit of a two digit number is 8 when we interchange the digits it is found that the resulting new number is greater than the original number by 18.

To find :-

• Two digit number

Solution :-

Let the tens digit be x then ones digit be y

• According to the first condition

Sum of the digit of a two digit number is 8

• Original number = 10x + y

→ x + y = 8

• According to second condition

When we interchange the digits it is found that the resulting new number is greater than the original number by 18.

• Reveresd number = 10y + x

→ 10x + y + 18 = 10y + x

→ 10x - x + y - 10y = - 18

→ 9x - 9y = - 18

→ 9(x - y) = - 18

→ x - y = - 2

Add both the equations

→ x + y + x - y = 8 - 2

→ 2x = 6

→ x = 3

Put the value of x in equation (ii)

→ x - y = - 2

→ 3 - y = - 2

→ y = 3 + 2

→ y = 5

Hence,

• Tens digit = x = 3
• Ones digit = y = 5

Therefore,

• Original number = 10x + y = 35
• Reversed number = 10y + x = 53

Answer 2

Answer:

$\underline{\boxed{\red{\bf Original \: number= 35}}}$

Step-by-step explanation:

Given,

• The sum of the digit of a two digit number is 8.
• When the digits are interchanged, the resulting new number is greater than the original number by 18.

To find,

• The original number.

Solution:

Let the digit at unit's place be x. And the digit at ten's place be y.

★ $\boxed{\bf Original \: number= 10x + y}$

It is given that, the sum of the digits is 8.

$\sf \implies x + y = 8 \: \: \:... (i)$

When the digits are interchanged,

★ $\boxed{\bf New \: number= 10y + x}$

According to the question,

$\sf \implies 10x + y +18= 10y + x$

$\sf \implies 10x - x + y - 10y=-18$

$\sf \implies 9x-9y=-18$

$\sf \implies 9(x-y)=-18$

$\sf \implies x-y=\dfrac{-18}{9}$

$\sf \implies x-y=-2 \: \: \:... (ii)$

Adding equation (i) and (ii), we get ;

$\sf \implies x+y+x-y= 8-2$

$\sf \implies 2x=6$

$\sf \implies x=\dfrac{6}{2}$

$\boxed{\bf \therefore x =3}$

Substituting the value of x in (i),

$\sf \implies x + y = 8$

$\sf \implies 3+ y = 8$

$\sf \implies y = 8-3$

$\boxed{\bf \therefore y =5}$

Now,

Original number = 10x + y

                            = 10 * 3 + 5

                            = 30 + 5

                            = 35

Hence, the original number is 35.