InterviewSolution
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InterviewSolution
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A three digit number is equal to 17 times the sum of its digits; If the digits ared, the new number is 198 more than the old number; also the sum ofdigits is less than the middle digit by unity. Find the original number.reversed, the new number is 198 more than the old number ; alsextreme |
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Answer» Let ones digit = x , tens digit = y , hundreds digit= zSo, number becomes = 100z+10y+xAccording 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 + z100z- z +10y-10y +x - 100x +198 = 099z - 99x +198 = 099x - 99z = 198 x - z = 2x = z + 2 ----------------------------(2) And, z + x = y-1By putting (2)y = z+z+2+1 y = 2z+3 ----------------------------(3) Putting (3) and (2) in (1) we get83z -7(2z+3) -16(z+2) = 0 83z -14z -21 -16z -32 = 053z = 53z = 1put z = 1 in (3)y = 2(1) +3y = 5 Put z = 1 in (2)x = 1+3= 3So. number = 100(1) + 10(5) + 3 = 153So, number = 153 |
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