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We know that P1V1=P2V2 by Boyle's Law. Let's say this equation (i).

And we know that V1/T1=V2/T2 by Charle's Law. Let this equation be (ii).

Dividing (i)/(ii), we get P1T1=P2T2...

But it's completely wrong as Gay-Lussac's Law says P1/T1=P2/T2

So where am I wrong ???

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Boyle's law is valid when temperature is constant. Charles law is valid when pressure is constant. If you are using both laws to deduce an equation in P and T, you have to assume that both pressure and temperature are constant. If you assume that, both Gay-Lussac's Law and the equation $P_1T_1=P_2T_2$ hold good.

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    $\begingroup$ But if P and T are constant, no change can happen, as the number of moles has not changed. $\endgroup$
    – Maurice
    Oct 2, 2021 at 8:04

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