Question

A three digit number is equal to 17 times the sum of its digits,if the digits are reversed,the new number is 198 more than the old number,Also the sum of the extreme digits is less than the middle digit by unity.Find the number.

Answer 1

Answer: THE NUMBER IS 153

Step-by-step explanation: suppose x be the

unit place and y be the tenth place . z be the digit in hundered p

lace . therefore the given three digits number 100z+10y+x by given condition 100z+10y+x=17(x+y+z) on solving it 83z-7y-16x=0 (eq 1) by second condition 100x+10y+z 100x+10y+z=100z+10y+x+198 on solving it x=2+z (eq 2) by third condition z+x=y-1 y=x+z+1 (eq 3) put eq 2 and eq 3 in eq 1 83z-7y-16x=0 83z-7(x+z+1)-16(2+z)=0 on solving it z=1 put z=1 in eq 2 on solving it we get x=3 again put z=1 and x=3 in eq 3 we get y=5 THE NUMBER IS 153