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A number consists of three digits, the right hand being zero. if the left hand and the middle digits are interchanged the number is diminished by 180. if the left hand digit is halved and the middle and the right hand digits are interchanged the number is diminished by 454. find the number.[hint. let the original number be 100a+10b+0, i.e., 100a+10b, then , by the first condition(100a+10b)-(100b+100a)= 180 = a-b=2by the second condition, new number= 100×a/2+0+b=50a+band so (100a+10b)-(50a+b)=454 = 50a+9b=454]​

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