Question

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





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Answer 1

Answer:

The digit

Step-by-step explanation:

The new number is greater than the old number by 27, i.e. Adding the two equations, we get 2y = 12 or y = 6. Thus, x = 3. Therefore, the original number is 36.

Answer 2

Step-by-step explanation:

Answer: The TWO digit number is 36

Let the two digits be X and Y

then X + Y = 9 ….. equation 1

By inter changing these digits it will be 10 Y + X

Then the difference of original number and inter changed digits will be

10 Y + X - ( 10 X + Y ) = 27

9 Y - 9 X = 27 or 9 ( Y - X ) = 27

Then Y - X = 3 ……. equation 2

By resolving equations 1 and 2 we will get

X = 3 and Y = 6

Hence the original number is 36 and interchanged number is 63 . The difference between these two numbers is 27

Let one of the digits= x

Then, other digit =9-x

Number= 10x + 9-x =9x +9

No. On interchanging the digits=10(9-x) +x

=90-10x + x = 90 -9x

According to the question,

Number1 + 27 = Number 2

= 9x +9 +27 = 90–9x

= 9x +36= 90–9x

= 9x+9x = 90-36

= 18x = 54

= x= 54/18

= x =3

Therefore other digit =9-x =9–3= 6

So the two digit number= 36