the sum of the digits of a two digit number is 13 the number formed by interchanging the digits is 45 more than the original number find the original number
Answers
Finding two digit Number
Answer: required original number is 49 .
Explanation:
Given that sum of digits of two digit number is 13.
And number formed by interchanging the digits is 45 more than the orignal number.
need to evaluate the orignal number.
lets assume digit at ones place by y
And digit at tens place by z .
so original number = Digit at tens place x 10 + digit at ones place
=> Original Number = z x 10 + y = 10z + y ----------eq (A)
On interchanging the digit , digit at ones place will come at tens place and digit at tens place will come at ones place
=> Interchanged number = y x 10 + z = 10y + z
As Interchanged number is 45 more that orignal number
=> Interchanged number - orignal number = 45
=> (10y + z ) - (10z + y) = 45
=> 10y +z -10z -y = 45
=> 9y - 9z = 45
=> 9( y - z ) = 45
=> y - z = 45/9
=> y-z = 5 ----------eq(1)
also given that sum of two digit is 13
=> y + z = 13 -----------eq(2)
On adding eq(1) and (2) , we get
(y-z) + ( y+z) = 5 + 13
=> y + y - z + z = 18
=> 2y = 18
=> y = 18/2 = 9
substituting y = 9 in eq(2) we get
9 + z = 13
=> z = 13 - 9 = 4
As y is digit at ones place and z is digit at tens place , we can say that required original number is 49 .
Also if you want to check , revere the number , we get 94 and 94 - 49 = 45.
Hence our solution is correct.
#anwerwithquality
#BAL
Answer:
fisksggsjhahusksjjsjs
Step-by-step explanation:
gsjsjjshshhdhdhhdhdhhd