Question

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

Answer 1

Step-by-step explanation:

Given :-

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.

To find :-

What is the two digit number ?

Solution :-

Let the digit at 10's place in the two digits number be X

The place value of X = X×10 = 10X

Let the digit at 1's place in the two digits number be Y

The place value of Y = Y×1 = Y

Then the number = 10X+Y

The Original number = 10X+Y

The number obtained by reversing the digits = 10Y+X

The New number = 10Y+X

Given that

Sum of the digits in the two digits number = 9

=> X+Y = 9 ------(1)

=> X = 9-Y ------(2)

and

When we interchange the digits,it is found that the resulting new number is greater than the original number by 27.

=> New number = Original number +27

=> 10Y+X = 10X+Y +27

=> 10Y+X-10X-Y = 27

=> 9Y-9X = 27

=> 9(Y-X) = 27

=> Y-X = 27/9

=> Y-X = 3

=> Y-(9-Y) = 3 (from (1))

=> Y -9+Y = 3

=> 2Y-9 = 3

=> 2Y = 3+9

=> 2Y = 12

=> Y = 12/2

=> Y = 6

On Substituting the value of Y in (1) the

=> X = 9-6

=>X = 3

Therefore, X = 3 and Y = 6

Answer:-

The Original number for the given problem is 36

Check:-

The Original number = 36

Sum of the digits = 3+6 = 9

New number obtained by reversing the digits = 63

=>63=36+27

=>New number = Original number+27

Verified the given relations in the given problem.

Used Method:-

• Substitution method

Answer 2

Step-by-step explanation:

a+b=9

Assume digit of unit's place =a

digit of ten's place=9-a

then the two digit number =10(9-a)+a

let us reverse the digit

then number becomes =10a+(9-a)

then the given condition is

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

9a+9=117-9a

18a=108

a=6

digit in ten's place=3

digit in unit's place=6

Hence the number is 36