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:

Let digit at ones place be y

and digit at tens place be x.

Number formed = 10x + y

Reverse Number = 10y + x

According to statement

x + y = 9.........(1)

Reverse number- Original number = 27

10y + x - 10x - y = 27

9y - 9x = 27

y - x = 3.......(2)

Adding (1) and (2) equations

2y = 12

y = 6.

Put y = 6 in (1)

6 + x = 9

=> x = 3

So number is 10×3 + 6 = 36