Question

The digits of a two-digit number differ by 3. If digits are interchanged and the

resulting number is added to the original number, we get 121. Find the original

number​

Answer 1

Given :

• The digits of a two digit number differ by 3

• The digits are interchanged and the resulting number is added to the original number, we get 121

To find :

• The original number

Solution :

Let the two digit number be 10x + y

where,

• x and y are the digits

According to the first condition given in the question :-

→ x - y = 3 ------(1)

Digits after interchanging :-

→ 10y + x

According to the second condition given in the question :-

→ 10x + y + 10y + x = 121

→ 11x + 11y = 121

→ 11(x + y) = 11

→ x + y = 11 ------(2)

Solving equation (1) and (2) :-

→ x - y = 3

→ x + y = 11

_________

→ 2x = 14

_________

→ 2x = 14

→ x = 14 ÷ 2

→ x = 7

→ The value of x = 7

Substitute the value of x in the equation (1) :-

→ x - y = 3

→ 7 - y = 3

→ - y = 3 - 7

→ - y = - 4

→ y = 4

→ The value of y = 4

The original number is :-

→ 10x + y

→ 10(7) + 4

→ 74