Question

-
Sum of the digits of a two-digit number (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?
MODEL II​

Answer 1

Answer:

let the digit at tens pkace be x and at ones place be y

then the number is 10x +y

when the digits are interchange the number is 10y +x

Now

x+y=9

y=9-x _______ eqn i

Again

10x + y +27 =10y + x

9x + 27 = 9y

putting value of y from eqn i

9x + 27 =9(9 - x)

9x+9 x = 81-27

x=54/18

• x=3

substituting the value of x in eqn i

• y = 9-3 =6

The number is 36.

Answer 2

Given

Sum of digits of two digit number = 9

Interchanged number is 27 greater than original number.

To find

Original two digit number

Solution

Let the digit at unit's place be a & digit at ten's place be b.

➙ Original number = a + 10b

➙ Interchanged number = b + 10a

According to 1st case :

➻ a + b = 9

➻ a = 9 - b ..(1)

According to 2nd case :

⟿ b + 10a = a + 10b + 27

➾ b + 10a - a - 10b = 27

⟿ 9a - 9b = 27

➾ 9(a - b) = 27

⟿ a - b = 27/9

➾ a - b = 3

• Putting value from (1)

⟿ 9 - b - b = 3

➾ -2b = 3 - 9

⟿ -2b = -6

➾ b = -6/-2

⟿ b = 3

Now putting value in (1)

➾ a = 9 - 3

⟿ a = 6

Now finding original two digit number :

➾ Original number = 6 + 10(3)

⟿ Original number = 6 + 30

➾ Original number = 36

Therefore,

Original two digit number = 36 .