Question

4]A two digit number is four times the sum of the digits. if 36 is added to the number, the digits

are reversed. find the numbers.​

Answer 1

Answer:

48

Step-by-step explanation:

Let the unit digit be 'y' and the tens digit be 'x'.Thus, the number be 10x + y.

⇒ number = 4 times sum of x and y

⇒ 10x + y = 4(x + y)

⇒ 6x = 3y      ⇒ 2x = y

If 36 is added to the number, the digits interchange their places. And the new number becomes 10y + x.

⇒ 10x + y + 36 = 10y + x

⇒ 36 = 9y - 9x

⇒ 36 = 9(2x) - 9x       [y = 2x ]

⇒ 36 = 9x

⇒ 4 = x

     Thus, y = 2x = 2(4) = 8

∴ Required number is xy = 48

Answer 2

Given :-

A two digit number is four times the sum of the digits. if 36 is added to the number, the digits  are reversed.

To Find :-

The numbers

Solution :-

Let

Unit digit = b

Tens digit = a

$\sf 10a+b =4a+4b$

$\sf 10a+b=4(a+b)$

$\sf 10a - 4a = 4b - b$

$\sf 6a = 3b$

$\sf \dfrac{a}{b} = \dfrac{6}{3}$

$\sf \dfrac{a}{b} = \dfrac{2}{1}$

2a = b

According to the question

$\sf 10a + b + 36 = 10b + a$

$\sf 36 = (10b-b)-(10a-a)$

$\sf 36 = 9b-9a$

Putting b =2a

$\sf 36 = 9(2a) - 9a$

$\sf 36 = 18a-9a$

$\sf 36 = 9a$

$\sf \dfrac{36}{9} = a$

$\sf 4 =a$

$\sf 2(4) = b$

$\sf 8 =b$