Question

the digit of a two digit number differ by 3 . if the digits are interchanged and the resulting number added to the original number , we get 121 . what is the original number ?​

Answer 1

Step-by-step explanation:

Let the tens digit of the number be x

And units digit be y

The original number = 10x + y

The number obtained by interchanging the digits = 10y + x

Case 1:-

The digits of the number differ by 3

⇢ x - y = 3......(i)

Case 2:-

Original number + Reversed number = 121

⇢ 10x + y + 10y + x = 121

⇢ 11x + 11y = 121

Dividing the whole equation by 11

⇢ x + y = 11......(ii)

Adding equations (i) and (ii)

⇢ x - y + x + y = 3 + 11

⇢ 2x = 14

⇢ x = 14/2 = 7

Substituting x = 7 in equation (ii)

⇢ x + y = 11

⇢ 7 + y = 11

⇢ y = 11 - 7 = 4

We have:-

• x = 7

• y = 4

The original number = 10x + y = 10(7) + 3 = 73

∴ The original number = 73

Answer 2

Answer:

• 10 (x + 3) + x = 10x + 30 + x = 11x + 30. It is given that the sum is 121. The units digit is 4 and therefore the tens digit is 4 + 3 = 7. Hence, the number is 74 or 47.

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