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A three digit number is equal to 17 times the sum of its digits ; If the digits are reversed, thenew number is 198 more than the old number, also the sum of extreme digits is less thanthe middle digit by unity. Find the original number. |
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Answer» ANSWER: 153 Step-by-step explanation: Let ones DIGIT = x , tens digit = y , hundreds digit = z So, number becomes = 100z+10y+x According to question- 100z+10y+x = 17(x+y+z) 100z+10y+x = 17X + 17y + 17z 100z-17z +10y-17y + x-17x = 0 83z -7y -16x = 0 -----------------------(1) Also, 100z+10y+x + 198 = 100x + 10y + z 100z- z +10y-10y +x - 100x +198 = 0 99z - 99x +198 = 0 99x - 99z = 198 x - z = 2 x = z + 2 ----------------------------(2) And, z + x = y-1 By PUTTING (2) y = z+z+2+1 y = 2z+3 ----------------------------(3) Putting (3) and (2) in (1) we get
83z -7(2z+3) -16(z+2) = 0 83z -14z -21 -16z -32 = 0 53z = 53 z = 1 put z = 1 in (3) y = 2(1) +3 y = 5 Put z = 1 in (2) x = 1+3= 3 So. number = 100(1) + 10(5) + 3 = 153 So, number = 153 |
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