Question

The sum of the digits of a two digits number is 7 the number obtained by interchanging the digits exceeds the original number by 27 find the no.

Answer 1

Answer:

25

Step-by-step explanation:

Let two digit number be : 10x+y

Given : x+y=7..........(1)

By interchanging digits , no will be 10y+x

Given :

10y+x=27+(10x+y)

10y+x=27+10x+y

10y-y=27+10x-x

9y=27+9x

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

but x+y=7 (from 1)

     y=7-x

putting this value in eq 2

7-x=3+x

7-3=x+x

4=2x

x=2 , y=5

The no is 10x+y =25

Answer 2

Given:-

• The sum of the digits of a two digit number is 7.
• The number obtained by interchanging the digits exceeds the original number by 27.

To find:-

• Find the numbers ?

Solutions;-

• Let the digit at the unit's place be 'y'
• Let the digit at ten's place be 'x'

NUMBER = 10x + y

The sum of the digits of a two digit number is 7.

=> x + y = 7

=> x = 7 - y .......(i).

The number obtained by interchanging the digits exceeds the original number by 27.

• Number obtained by reversing the digits = 10y + x
• Number obtained by reversing the digits = Original number + 27

=> 10y + x = 10x + y + 27

=> -27 = 10x - x + y - 10y

=> -27 = 9x - 9y

=> -27 = 9(x - y)

=> -27/9 = x - y

=> -3 = x - y ......(ii).

Putting the value of 'x' in equation (ii).

=> -3 = x - y

=> -3 = 7 - y - y

=> - 3 = 7 - 2y

=> -3 - 7 = -2y

=> -10 = -2y

=> -10/-2 = y

=> 5 = y

=> y = 5

Putting the value of 'y' in equation (i).

=> x = 7 - y

=> x = 7 - 5

=> x = 2

Now,

Number = 10x + y

=> 10(2)+5

=> 20+5

=> 25

Hence, the number is 25.