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 × 1 + 4) = 9
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5 | y - 1         x = (4 × y + 1) = (4 × 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
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   | 1 - 3
Respective remainders are 2 and 3