Question

d two digit number
4 times the sum of the
digits. 36 is added to
th u ller the digits are
reverse. Find the numbers?​

Answer 1

Answer:

The Original Number is 48.

Step-by-step explanation:

Given :

The number = 4 times the sum of its digits

When 36 is added to the number = the digits get interchanged

To find :

The Original Number

Solution :

$\textsf{\underline{\underline{Let the digits be - }}}$

• Tens Place as x
• Units Place as y

⇒ 10(x) + y

⇒ 10x + y ..........(Original Number)

$\rule{300}{1.5}$

$\textsf{\underline{\underline{Number with interchanged digits -}}}$

• Tens Place as y
• Units Place as x

⇒ 10(y) + x

⇒ 10y + x .........(Number with Reversed Digits)

$\rule{300}{1.5}$

$\textsf{\underline{\underline{According to the Question -}}}$

Two digit number = 4 times the sum of its

Two digit number = 4 times the sum of itsdigits

⇒ 10x + y = 4(x + y)

⇒ 10x + y = 4x + 4y

⇒ 10x - 4x = 4y - y

⇒ 6x = 3y

⇒ 2x = y .............(1)

$\rule{300}{1.5}$

When 36 is added to the original number the digits of the number get reversed.

⇒ 10x + y + 36 = 10y + x

⇒ By Substitution

⇒ 10x + 2x + 36 = 10(2x) + x

⇒ 12x + 36 = 20x + x

⇒ 12x + 36 = 21x

⇒ 21x - 12x = 36

⇒ 9x = 36

⇒ x = $\sf{\dfrac{36}{9}}$

⇒ x = 4

$\rule{300}{1.5}$

★ 2x = y

⇒ 2(4) = y

⇒ 8 = y

$\rule{300}{1.5}$

★ Original Number -

⇒ 10x + y

⇒ 10(4) + 8

⇒ 40 + 8

⇒ 48

Original Number = 48

$\therefore$ The Original Number is 48.