The digit of a two digit number 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?
Answers
For any two digit, the sum of the two digit number and the two digit number got by interchanging its digits, is the product of sum of digits and 11.
If the number is 10x + y, then,
(10x + y) + (10y + x) = 11(x + y).
Here, 11(x + y) = 143.
x + y = 143 ÷ 11 = 13 ⇒ (1)
x - y = 3 OR y - x = 3 ⇒ (2)
Consider x - y = 3.
(1) + (2)
= (x + y) + (x - y) = 13 + 3
= x + y + x - y = 16
= 2x = 16
x = 16 ÷ 2 = 8
(1) - (2)
= (x + y) - (x - y) = 13 - 3
= x + y - x + y = 10
= 2y = 10
y = 10 ÷ 2 = 5
∴10x + y = 10 × 8 + 5 = 80 + 5 = 85.
If y - x = 3 is considered, we get x = 5 and y = 8.
∴ 10x + y = 10 × 5 + 8 = 50 + 8 = 58.
So the answer is either 85 or 58.
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