Question

The sum of digits of a two digit number is 8. If 18 added to the number then it is equal to the reversing the digits of the number the find the number?​

Answer 1

Answer:

• The number will be 35

Explanation:

Let, the unit digit of number be y and tens digit be x

then,

the number will be

• 10 x + y

so,

→ x + y = 8

→ x = 8 - y   _______equation (1)

On adding 18 to the number its digits are reversed

so,

the reversed number will be

• 10 y + x

so,

→ 10 x + y + 18 = 10 y + x

→ 10 x - x + y -10 y + 18 = 0

→ 9 x - 9 y  +18 = 0

dividing by 9 both sides

→ x - y + 2 = 0

using equation (1)

→ 8 - y - y + 2 = 0

→ - 2 y = - 10

→ y = 5

putting value of y in equation (1)

→ x = 8 - y

→ x = 8 - ( 5 )

→ x = 3

therefore,

the actual number will be

→ 10 x + y

→ 10 ( 3 ) + 5

→ 30 + 5

→ 35

therefore,

• The actual number is 35 .

Answer 2

$\huge\mathcal{\underbrace{\red{SOLUTION:-}}}$

GIVEN :-

• The sum of digits of a two digit number is 8 .

• If 18 added to that number, then that is equal to the reversing the digits of the number .

TO FIND :-

• The Original Number .

CALCULATION :-

✍️ Let, the unit(ones) digit be ‘x’ .

And the tens digit be ‘y’ .

✍️ So, the original number be ‘10y + x’ .

✍️ According to the question,

• x + y = 8 .

• => x = 8 - y -----(1)

✍️ If 18 added to the number, then the number is

• ‘10y + x + 18’ .

✍️ And if we reversing the original number, then the resulting number is

• ‘10x + y’ .

✍️ According to the question,

$\rm{\implies\:10y\:+\:x\:+18\:=\:10x\:+\:y\:}$

$\rm{\implies\:9x\:-\:9y\:=\:18\:}$

$\rm{\implies\:9\:(x\:-\:y)\:=\:18\:}$

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

✍️ Now, putting the value of ‘x’ from equation(1)

$\rm{\implies\:8\:-\:y\:-\:y\:=\:2\:}$

$\rm{\implies\:8\:-\:2y\:=\:2\:}$

$\rm{\implies\:2y\:=\:8\:-\:2\:}$

$\rm{\implies\:y\:=\:\dfrac{6}{2}\:}$

$\rm{\blue{\implies\:y\:=\:3\:}}$

✍️ Put the value of y in equation (1),

$\rm{\implies\:x\:=\:8\:-\:3\:}$

$\rm{\blue{\implies\:x\:=\:5\:}}$

$\therefore$ The original Number is,

$\rm{=\:10y\:+\:x\:}$

$\rm{=\:10\times{3}\:+\:5\:}$

$\rm{=\:30\:+\:5\:}$

$\rm{=\:35}$

$\therefore$ $<font color=green>$ The original number is “35” .