5. A number consists of three digits, the right hand being zero. If the left hand and the middle digits be

interchanged the number is diminished by 180. If the left-hand digit be halved and the middle andright-hand digits be 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 + 10a) = 180 = a-b= 2By the second condition, new number = 100 +0+ b = 50a + b2and so (100a+10b) – (50a + b) = 454 = 50a +9b = 454].a