Question

A two-digit number is three times the sum of
its digits. If 45 is added to the number, its
digits are interchanged. The sum of the digits
of the number is:

​

Answer 1

Answer:

The sum of the digits is 9

Step-by-step explanation:

Let the original no. be xy

So, the number is 10x + y

10x + y = 3(x + y)

10x + y + 45 = 10y + x

When solving, you will get the values for x and y respectively

Answer 2

The question comprises of two data.

Data 1 :

A two-digit number is three times the sum of its digits

Data 2:

If 45 is added to the number, it's digits are reversed.

_____________________________________________________

Let us consider that,

Two digit number = 10x + y

x, y are digits.

From data 1 ;

⇒10x + y = 3 ( x + y)

⇒10x + y = 3x + 3y

⇒ 10x - 3x + y - 3y = 0

⇒7x - 2y = 0

From data 2 ;

⇒ 10x + y + 45= 10y + x

⇒ 9x - 9y = - 45

⇒ x - y = - 5

We have two equations now,

7x - 2y = 0

2x - 2y = - 10

⇒5x = 10

⇒ x = 2

Substituting in any equation, We get

⇒x - y = - 5

⇒2 - y = - 5

⇒2 + 5 = y

⇒y = 7

Therefore, The two digit number is 10(2)+7 = 27