Question

sum of a digit of a 2 no.is 9.When we interchange the digits,it is found that the resulting by 27.What is the two digit no?​

Answer 1

Answer:

original number is 36.

Step-by-step explanation:

let the digits be x & y.

hence number is 10 x + y .

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

by interchanging digits number will become ,

10 y + x .

it is increased by 27.

means,

10x+y+27=10y + x

9 x + 27 = 9y

9y-9x=27

(y-x)=27/9

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

adding equation (1) & (2),

x+y+y-x=9+3

2y=12

y=6

substituting y=6 in equation (1),

x+y=9

x+6=9

x=3

number =10×3+6=36.

hope it is helpful.

Answer 2

$\bold{\huge{\fbox{\color{Black}{Given}}}}$

• Sum of two digits = 9

• Difference of two Numbers = 27

$\bold{\huge{\fbox{\color{Black}{ToFind}}}}$

• Two digit number

$\bold{\huge{\fbox{\color{Black}{Solution}}}}$

Let

• Tens digit be x

• Ones digit be y

• Then, number is = 10x + y

Digits interchanged ,

Ones place digit interchange tens place digit

So,

• New number is = 10y + x

Now,

According to Question :-

1st Case:

• => x + y = 9

• => x = 9 - y. -----(1)

2nd Case:

• => 10x + y - (10y + x) = 27

• => 10x + y - 10y - x = 27

• => 9x - 9y = 27

• => 9(x - y) = 27

• => x - y = 27/9 = 3

• => x - y = 3. ----(2)

Put the value of x from (1) in (2),we get

• => ( 9 - y) - y = 3

• => 9 - 2y = 3

• => 2y = 9 + 3 = 12

• => y = 12/2 = 6

Then,

• => x = 9 - y = 9 - 6 = 3

Hence,

Number is 10x + y = 10×3 + 6 = 30+ 6=36

Interchanged no = 10y + x = 10×6 +3 = 60+3 =63