Question

If 45 is added to the number, the digits are reversed. A 2-digit number is 5 more than 3 times the sum of its digits. Find the number.​?

Answer 1

Answer:

9 is the correct answer

Step-by-step explanation:

Answer 2

$\huge \red {\boxed {\boxed {\mathbb {QUESTION}}}}$

If 45 is added to the number, the digits are reversed. A 2-digit number is 5 more than 3 times the sum of its digits. Find the number.?

$\huge \purple {\boxed {\boxed {\mathbb {ANSWER}}}}$

$\huge \blue {\underline {\underline {\mathbb {Orginal \:Number \:will\: be 38.}}}}$

$\huge \red {\boxed {\boxed {\mathbb {EXPLAINATION}}}}$

Let the Number be (10x + y) where y is One's Digit and x is Ten's Digit.

☢ According to the Question Again :

↠ Number = 5 + 3(Sum of Digits)

↠ (10x + y) = 5 + 3(x + y)

↠ 10x + y = 5 + 3x + 3y

↠ 10x – 3x + y – 3y = 5

↠ 7x – 2y = 5 ⠀— eq.( I )

___________________

☢ According to the Question Again :

↠ Original No. + 45 = Reverse No.

↠ (10x + y) + 45 = (10y + x)

↠ 10x + y + 45 = 10y + x

↠ 10x – x + y – 10y + 45 = 0

↠ 9x – 9y + 45 = 0

↠ 9x – 9y = – 45

↠ 9(x – y) = – 45

Dividing both term by 9

↠ x – y = – 5

↠ x = (y – 5) ⠀— eq.( II )

━━━━━━━━━━━━━━━━━━━━

★ Putting the value of x in eq. ( I ) :

⇢ 7x – 2y = 5

⇢ 7(y – 5) – 2y = 5

⇢ 7y – 35 – 2y = 5

⇢ 5y = 5 + 35

$\huge \green {\boxed {\boxed {\mathbb { ⇢ 5y = 40 }}}}$

• Dividing both term by 5

$\huge \blue {\boxed {\boxed {\mathbb { ⇢ y = 8 }}}}$

________________________

★ Putting the value of y in eq. ( II ) :

⇢ x = (y – 5)

⇢ x = (8 – 5)

$\green {\boxed {\boxed {\mathbb { ⇢ x = 3 }}}}$

◗ Number = (10x + y) = (10 × 3 + 8) = 38

∴ Therefore, Orginal Number will be 38.

$\huge \green {\boxed {\boxed {\underline {\mathbb {SINGLE\:STAR}}}}}$