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
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.
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