Question

The digits of a two numbers 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

Answer:

Let the tens digit of two digit no. be x and unit digit be y.

Required no. 10x+y

x-y=3 -----------1

10x+y+10y+x=143

11x+11y=143

11(x+y)=143

x+y=143/11

x+y=13 -----------2

Adding 1 and 2

x+y+x-y=13+3

2x=16

x=8

Putting x=8in 2

8+y=13

y=5

Answer 2

$\sf{\huge{\underline{\green{Given :-}}}}$

• The digits of a two numbers differ by 3.

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

$\sf{\huge{\underline{\green{To\:Find :-}}}}$

• The original number.

$\sf{\huge{\underline{\green{Answer :-}}}}$

Let us consider the number be xy,

Such that, x at tens place & y at once place.

x > y

According to the question,

The digits of a two numbers differ by 3.

x - y = 3 ------(1)

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

• The number = 10x + y

• The reversed number = 10y + x .

➝ 10x + y + 10y + x = 143

➝ 10x + x + 10y + y = 143

➝ 11x + 11y = 143

➝ x + y = 13 ------(2)

From equation 1 & 2,

x - y = 3

x + y = 13

________

2x = 16

_______

➝ x = 16/2

➝ x = 8

putting in equation 1,

x - y = 3

➝ 8 - y = 3

➝ - y = 3 - 8

➝ - y = - 5

➝ y = 5

The original number = 10x + y = 10 × 8 + 5 = 80 + 5 = 85

So, The original number is 85 .