Question

sum of the digits of a two digits no.is 9 the no.obtained by inter changeing the digits exceeds the given number by 27 find the given no.,ans is 36

Answer 1

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Answer 2

Assume the digit in ones place as x and the digit in tens place is y The original number is (10y + x) Number obtained by reversing the digits = (10x + y) Now check for the condition Given that sum of digits of the number is 9 That is x + y = 9   → (1)Second condition is, number obtained by interchanging the digits is greater than the original number by 27 That is
(10x + y) = (10y + x) 27 
⇒ 10x + y – 10y – x = 27 
⇒ 9x – 9y  = 27 
⇒ 9(x – y) = 27
⇒x – y = 27/9
∴ x – y = 3
→ (2) Add (1) and (2),
we get x + y = 9 x – y = 3 ----------- 2x = 12 ∴ x = 6 Put x = 6 in (1), we get 6 + y = 9⇒ y = 9 – 6 = 3 The original number = 10y + x = 10(3) + 6 = 36