Question

The digits of a two digit number differ by 3 . If the digits are interchanged and the resulting number is added to the original number, we get 143. what can be the original number​

Answer 1

$\Large\underline\mathbf{Given:-}$

• The digits of a two digit number differ by 3.
• If the digits are interchanged and the resulting number is added to the original number, we get 143.

$\Large\underline\mathbf{To \: Find:-}$

• What is the original number?

$\Large\underline\mathbf{Solution:-}$

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

◆ NUMBER = 10x + y

$\large{\underline{\underline{\mathsf{\red{Case:-1)}}}}}$

✒ The digits of a two digit number differ by 3.

${\underline{\bf{According \: To \: Question:-}}}$

➺ x –y = 3

➺ x = 3 + y....1)

$\large{\underline{\underline{\mathsf{\red{Case:-2)}}}}}$

✒ If the digits are interchanged and the resulting number is added to the original number, we get 143.

◘ Reversed Number = 10y + x

❮Reversed Number + Original Number = 143❯

${\underline{\bf{According \: To \: Question:-}}}$

➺ 10x + y + 10y + x = 143

➺ 11x + 11y = 143

'Taking common 11 from both sides'

➺ x + y = 13....2)

Put the value of x in equation 2), we get

➺ 3 + y + y = 13

➺ 3 + 2y = 13

➺ 2y = 13 –3

➺ 2y = 10

➺ y = $\sf{\cancel\dfrac{10}{2}}$

$\longmapsto$ $\large{\underbrace{\mathbf{\red{ \: y = 5 \: }}}}$

Put the value of y in equation 1), we get

➺ x = 3 + 5

$\longmapsto$ $\large{\underbrace{\mathbf{\red{ \: x = 8 \: }}}}$

❍ NUMBER = 10x + y

❍ NUMBER = 10(8) + 5

❍ NUMBER = 80 + 5

❍ NUMBER = 85

❝ Hence, the number formed is 85 ❞

______________________

Answer 2

Answer:

Let the unit digit be x and tens digit be x + 3

Therefore, the original number = 10(x + 3) + x

On interchanging, the number formed = 10x + x + 3

❍ According to Question now,

➥ 10(x + 3) + x + 10x + x + 3 = 143

➥ 10x + 30 + 12x + 3 = 143

➥ 22x + 33 = 143

➥ 22x = 143 - 33

➥ 22x = 110

➥ x = 110/22

➥ x = 5

__________________...

Therefore,

• The unit digit number = x = 5

• The tens digit number = x + 3 = 5 + 3 = 8

__________________...

• The original number = 10(x + 3) + x

• The original number = 10(5 + 3) + 5

• The original number = 50 + 30 + 5

• The original number = 85

Hence,the original number is 85.