Question

Sum of digit of 2 digit is9 when we interchange the digit it is found that the resulting new number is greater than the original number by 27 what is the two digit number

Answer 1

the answer is 36. simply look out for all posible 2 digit nos whose total is 9 and who lie in close proximity of under 30 with each other.

Answer 2

Answer :

Let the unit place digit be x
& ten place digits be y

Then number = 10y + x

A. T. Q

Case-1
Sum of digit = 9
x + y = 9 or x = 9 - y

Case-2
Interchange the places
New number = 10x + y

New number = 27 + original number
10x + y = 27 + 10y + x
10x - x + y - 10y = 27
9x - 9y = 27
9(x-y) = 27
x - y = 27/9
x - y = 3

From equation 1
9 - y - y = 3
9 - 2y = 3
-2y = 3 - 9
-2y = -6
y = 6/2
y = 3

From Equation 1
x = 9 - y
x = 9 - 3
x = 6

Then the number = 10y + x
= 10×3 + 6
= 30 + 6
= 36

Hence 36 is the two digit number


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