A number when divided successively by 4 and 5 leaves remainders 1 and 4 respectively. When it is successively divided by 5 and 4, then the respective remainders will be

 4 | x            y = (5 x 1 + 4) = 9
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 5 | y -1         x = (4 x y + 1) = (4 x 9 + 1) = 37
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   | 1 -4

 Now, 37 when divided successively by 5 and 4, we get

 5 | 37
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 4 | 7 - 2
 ---------
   | 1 - 3
 
 Respective remainders are 2 and 3.