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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?

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? 

Grade:12

1 Answers

Harshit Singh
askIITians Faculty 5963 Points
one year ago
Dear Student

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
Originalnumber=10x+(9-x)=(10×3)+(9-3)=30+6=36
Thus, the number is 36.

Thanks

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