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15. A three digit number is equal to 17times the sum of its digits. If the digits.are reversed, the new number is 198more than the old number; also thesum of extreme digits is less than themiddle digit by unity. Find theoriginal number. |
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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 + 17z100z-17z +10y-17y + x-17x = 083z -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 = 2 x = z + 2--------------------(2) And, z + x = y-1By putting (2)y = z+z+2+1 y = 2z+3 ----------------------(3) Putting value of y from eq(3) and x from eq(2) in (1) we get 83z -7(2z+3) -16(z+2) = 0 83z -14z -21 -16z -32 = 053z = 53z = 1put z = 1 in eq(3)y = 2(1) +3y = 5 Put z = 1 in eq(2) x = 1 + 3 = 3So, number = 100(1) + 10(5) + 3 = 153 Therefore, number = 153 |
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