SOLUTION: 20) the tens digit of a three-digit number exceeds the hundreds digit by the same amount that the units digit exceeds the tens digit. When the digits are reversed, the new number e

Question 23582: 20) the tens digit of a three-digit number exceeds the hundreds digit by the same amount that the units digit exceeds the tens digit. When the digits are reversed, the new number exceeds the original numer by 198. Find the number.thank you!!
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
LET THE ORIGINAL NUMBER BE HTU WITH H IN HUNDREDS DIGIT ,T IN TENS DIGIT AND U IN UNITS DIGIT....ITS VALUE =100H+10T+U
the tens digit of a three-digit number exceeds the hundreds digit by the same amount that the units digit exceeds the tens digit. When the digits are reversed, the new number exceeds the original numer by 198. Find the number.thank you!!
TENS DIGIT EXCEEDS HUNDREDS DIGIT BY T-H
UNITS DIGIT EXCEEDS TENS DIGIT BY U-T
THESE ARE SAME .HENCE
T-H=U-T...OR 2T=U+H..................................................I
WHEN DIGITS ARE REVERSED TNE NEW NUMBER BECOMES
UTH...ITS VALUE = 100U+10T+H
NEW NUMBER EXCEEDS ORIGINAL NUMBER BY =100U+10T+H-100H-10T-U
=99U-99H=99(U-H)
THIS IS EQUAL TO 198
HENCE 99(U-H)=198
U-H=198/99=2.........................................................II
U+H=2T..................FROM....I
ADDING,WE GET
2U=2T+2.....DIVIDING BY 2,WE GET
U=T+1...OR........T=U-1......................AND
H=U-2...........FROM.......II
SO THE ORIGINAL NUMBER IS
HTU = (U-2)(U-1)U...NOW SINCE U IS NOT SPECIFIED WE CAN HAVE VARIOUS VALUES FOR U STARTING FROM 9 TO 2...SINCE U-2 CANNOT BE NEGATIVE..SO THE SOLUTIONS ARE
U=9..........789.............987-789=198
U=8...........678............876-678=198...ETC
U=7..........567
U=6..........456
U=5............345
U=4............234
U=3............123
U=2.............012...WE MAY DISCARD THIS ALSO AS IT CANOT BE CONSIDERED AS 3 DIGIT NUMBER,THOUGH THIS ALSO SATISFIES THE CONDITION THAT 210-12=198

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