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Home / Doubts and Solutions/MAHARASHTRA OLD/Class 10/Mathematics

A three digit number is equal to 17 times the sum of its digits. If 198 is added to the number , the digits are interchanged. The addition of first and third digit is 1 less than middle digit. Find the number

Asked by rajeshbhedaoo 9th March 2016, 12:05 AM
Answered by Expert
Answer:
begin mathsize 16px style L e t space t h e space t h r e e minus d i g i t space n u m b e r space b e space x y z.. I t s space n u m e r i c a l space v a l u e space equals space 100 x plus 10 y plus z A c c o r d i n g space t o space f i r s t space i n f o r m a t i o n space p r o v i d e d space i n space t h e space q u e s t i o n comma 100 x plus 10 y plus z equals 17 left parenthesis x plus y plus z right parenthesis rightwards double arrow 100 x plus 10 y plus z equals 17 x plus 17 y plus 17 z rightwards double arrow 83 x minus 7 y minus 16 z equals 0 space space space space space.... left parenthesis 1 right parenthesis N u m b e r space o b t a i n e d space b y space r e v e r sin g space t h e space d i g i t s colon space z y x I t s space n u m e r i c a l space v a l u e equals 100 z plus 10 y plus x A c c o r d i n g space t o space s e c o n d space i n f o r m a t i o n space p r o v i d e d space i n space t h e space q u e s t i o n comma left parenthesis 100 x plus 10 y plus z right parenthesis plus 198 equals 100 z plus 10 y plus x rightwards double arrow 99 z minus 99 x equals 198 rightwards double arrow z minus x equals 2 space space space space space rightwards double arrow z equals x plus 2 space space space.... left parenthesis 2 right parenthesis A c c o r d i n g space t o space t h i r d space i n f o r m a t i o n space p r o v i d e d space i n space t h e space q u e s t i o n comma x plus z equals y minus 1 space rightwards double arrow x plus x plus 2 equals y minus 1 space space space space space space.... left parenthesis f r o m space left parenthesis 2 right parenthesis right parenthesis rightwards double arrow y equals 2 x plus 3 space space space S u b s t i t u t i n g space z space a n d space y space i n space left parenthesis 1 right parenthesis comma 83 x minus 7 left parenthesis 2 x plus 3 right parenthesis minus 16 left parenthesis x plus 2 right parenthesis equals 0 rightwards double arrow 83 x minus 14 x minus 21 minus 16 x minus 32 equals 0 rightwards double arrow 53 x minus 53 equals 0 rightwards double arrow 53 x equals 53 rightwards double arrow x equals 1 rightwards double arrow y equals 2 x plus 3 equals 2 left parenthesis 1 right parenthesis plus 3 equals 2 plus 3 equals 5 rightwards double arrow z equals x plus 2 equals 1 plus 2 equals 3 T h u s comma space t h e space t h r e e minus d i g i t space n u m b e r space i s space 153. space space space space end style
Answered by Expert 9th March 2016, 11:49 AM
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