Question

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

Answer 1

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Answer 2

Questions

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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.

$\huge{\boxed{\sf Solution}} </p><p>$

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

Hence Verified