Question

The sum of the digits of a two digit number is 12. If the new number formed by reversing the digits is greater than the original number by 54,find the original number.Check your solution.

Answer 1

Given sum of the digits is 12 Let the digits in ones place be x Hence the digit in tens place is (12 – x) The original number = 10(12 – x) + x = 120 – 9x Number formed by reversing the digits = 10x + (12 – x)  =  9x + 12 Given that number formed by reversing the digits is 54 greater than the original number. ⇒ 9x + 12 = (120 – 9x) + 54 = 174 – 9x ⇒ 18x = 174 – 12 = 162 ∴ x = 9 The original number = 120 – 9x = 120 – 9(9) = 39...
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Answer 2

let the digit in one's place be x
let the digit in tens place be y

first condition

(y*10)+x = 12.....(1)

2nd condition

(x*10)+y=54+ (y*10)+x.....(2)

solve 1 and 2 to obtain your answer