Question

sum of the two digits of a 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 d no. be 10x+y

I condition

x+y=9

=>y=9-x.........1

II condition

10y+x=10x+y+27

9y-9x=27

y-x=3

9-x-x=3 (from 1)

-2x=-6

x=3

Subs x in 1

y=9-3

y=6

Therefore the no. Is 36

Hope it helps u

Answer 2

Given that sum of the two digits is 9.

Let us assume the digit of units place be x.

Then the digit of tens place will be 9-x.

Thus the two digit number is 10(9-x) + x

Now if we reverse the digits, the number becomes 10x + (9-x).

As per the question,

10x + (9-x) = 10(9-x) + x + 27

or 9x + 9 = 90 - 10x + x + 27

or 9x + 9 = 117 - 9x

Transposing -9x to the LHS and 9 to the RHS:

9x + 9x = 117 - 9

or 18x = 108

x = 6

Thus two digit number is 36.