Question

sum of the digits of a two-digit number is 9 then we interchange the digits it is found that the resulting new number is greater the original number by 27 what is the two digit number

Answer 1

Let the two digits of the number be x and y.

x+y = 9 …(1)

(10x+y)-(10y+x) = 27, or

9x-9y = 27, or

x-y = 3 …(2)

Add (1) and (2)

2x = 12, or x = 3, so y = 9–6 = 3.

So the original number is 36 which on reversing becomes 63 and 63–36 = 27. Correct.

Answer 2

Answer :

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

then number = 10y + x

A. T. Q

Case 1 - Sum of digit = 9
x + y = 9
Or x = 9 + y ------------ Equation 1

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

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