Question

the sum of digit of2 digit number is 9 if 27 is substracted from the number we get a 2 digit number qith the sequence of digit change find the no

Answer 1

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

∴ x – y = 3 → (2)

Add (1) and (2), we get

x + y = 9

x – y = 3

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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