Question

The tens digits of a two-digit number exceed the unit digits by 5. If the digits are reversed , the new number is less by 45. If the sum of digits is 9, find the numbers.

Answer 1

Let the digit in the units place be x

Hence the digit in the tens place is (x+5)

The original number =10(x+5)+x=11x+50

Number formed by reversing the digits =10x+(x+5)=11x+5

Given that:- (11x+50)-(11x+5)=45

Also, sum of digits = 9

⇒ x+ x+5 =9

⇒ x = 2

∴ Original number =11x+50=11(2)+50=72

Hence the original number is 72.

Hence the correct answer is 72.