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Linear Equations in One Variable
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05/08/2021 12:14 pm
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Sum of the digits of a two-digit number is 9. When we interchange the digits, it is found that the resulting new number is greater than the original number by 27. What is the two-digit number?
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05/08/2021 12:15 pm
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.