Question

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 original number by 27 . What is the two digit number?

Answer 1

Given

Sum of the digits of a two digit number is 9.

$\implies x+y=9--(1)$

When we interchange the digits, it is found that the resulting new number is greater than original number by 27.

$\implies 10y+x=10x+y+27\\\implies -10x+x+10y-y=27\\\implies -9x+9y=27\\\implies -x+y=3--(2)$

Solving (1) and (2), we get,

$x+y=9\\\underline{-x+y=3}\\\implies \underline{\underline{2y=12}}\\\implies y = 6\\\implies x = 3$

$\boxed{\boxed{\bold{Therefore, \ the \ required \ number \ is \ 36}}}}}}}}}$

                                                                           

Answer 2

Answer:

SOLUTION ::

Let unit place = b, ten place = a

So the number is 10a+b

Now by the given condition

a+b=9 - - - - - - - - (1)

when number’s digits are reversed then resulting number is 10b + a

Since the number formed by reversing the digits is less than the original number by 9

( 10b +a) - (10a + b) = 27

➙ 9a - 9b = - 27

➙ a - b = - 3- - - - - - - (2)

Adding Equation (1) & Equation (2)

2a = 6

➙ a = 3

From Equation (1)

b = 9 - 3 = 6

So the original number is = (10×3) + 6 = 36

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