Digits 5. A number consists of three digits, the right-hand digit 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 and
right-hand digits be interchanged the number is diminished by 454. Find the number.
[Hint. Let the original number be 1000 + 10b + 0, i.e., 100a + 10b, then, by the first condition
(100a+10b) -(100b + 10a) = 180 = a - b = 2
By the second condition, new number = 100 x = +0+ b = 50 a + b
2
and so (100a+10b) - (50a + b) = 454 > 50a + 9b = 4541
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