Question

The digits of a 2 digit number differ by 3. If digits are interchanged the resulting number is added to the original number, we get 121 . Find the original number?

Answer 1

The original number is 74

Answer 2

Answer:

The required Number is 74.

Step-by-step explanation:

$\huge{\boxed{\sf To Find}}$

The digits of a 2 digit number differ by 3, if the digits are interchanged and the resulting number is added to the original number we get 121.

$\huge{\boxed{\sf Solution}}$

Let the digits of the number be a and b such that the number is (10a+b).

According to the question,

➡ a − b = 3 ...... (1)

➡ 10a + b + 10b + a = 121

➡ 11a + 11b = 121

➡ a + b = 11 ...... (2)

Add (1) and (2) , we get

➡ a - b + a + b = 3 + 11

➡ 2a = 14

➡ a = 7

Substitute a = 7 in equation 2 , we get

➡ 7 + b = 11

➡ b = 11 - 7

➡ b = 4

Now, we have to find the numbers

➡ 10a + b

➡ 10(7) + 4

➡ 70 + 4

➡ 74

$\boxed{Hence, the required Number is 74.}$

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