Math, asked by amanbalara567, 11 months ago

3. The sum of the digits of a 2 digit number is 9. By interchanging the places of the diglia, the number
reduces by 63. Find the original number.​

Answers

Answered by upadanrtm2020
1

Finding two digit number

Answer:Required original number is 81 .

Explanation:

Given that

Sum of the digits of two digit number is 9

By interchanging the places the number reduces by 63.

Need to determine orignal number.

lets assume digit at ones place = y

And digit at tens place = z

Orignal number = 10 x digit at tens place + digit at ones place

=> Orignal Number = 10 x z + y = 10z + y

On interchaginf the digit , digit at ones place comes at tens place and digit at tens place comes at ones place

=> Interchage number = 10 x y + z = 10y + z

As number is reduced by 63 on interchanging

=> Orignal number -  Interchage number  = 63

=> (10z + y ) - ( 10y + z ) = 63

=> 10z +y - 10y - z = 63

=> 9z -9y = 63

=> 9(z - y) = 63

=> z - y = 63/9

=> z - y = 7   -------eq (1)

Also given sm of two digits is 9

=> z + y = 9 --------eq (2)

On adding eq(1) and eq(2) , we get

=> (z - y ) + ( z + y ) = 7 + 9

=>  z + z - y + y = 16

=> 2z = 16

=> z = 16/2 = 8

Subtituting value of z in equation 2 we get

8 + y = 9

=> y = 9 - 8 = 1

As digit at tens place is z = 8 and digit at ones place is y = 1  , so orignal number is 81 .

we can also check by interchaginf the number . On interchaging we get 18 and 81 - 18 = 63 . Hence our solution is correct.

#answerwithquality

#BAL

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