Successive Divisions

Algebra Level 3

A number \(N\) when successively divided by \(3,5\) and \(8\) leaves remainders \(1,4\) and \(7\) respectively. The same number \(N\) when successively divided by \(8, 5\) and \(3\) leaves remainder \(p, q\) and \(r\) respectively. Find \(100p+10q+r\).

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