Sum of the digits of a two- digits number is 7. When we interchange the digits, it is found that the resulting new number is greater than the original number by 9. What is the two – digit number?
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Let the digit at tens place be x then digit at ones place will be (9-x).
Original two digit number = 10x + (9-x)
After interchanging the digits, the new number = 10(9-x) + x
According to the question,
10x + (9-x) + 27 = 10(9-x) + x
⇒ 10x + 9 - x + 27 = 90 - 10x + x
⇒ 9x
+36 = 90 - 9x
⇒ 9x + 9x = 90 - 36
⇒ 18x = 54
⇒ x = 3
Original number = 10x + (9-x) = (10×3) + (9-3) = 30 + 6 = 36
Thus, the number is 36.
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