how n1t1/p1 =n2t2/p2is derived from the gas equation which is pv=nrt

Dear student,

We have PV = nRT, on rearranging - PV/ nT = R.
If 2 different conditions are given , then we have- $\frac{P_1{V}_1}{n_1{T}_1}= \frac{P_2{V}_2}{n_2{T}_2}$ ( as R is constant)
If V is constant for given condition then V1 = V2, therefore above equation becomes
$$\begin{gathered} \frac{P_1}{n_1{T}_1}=\frac{P_2}{n_2{T}_2} or \\ \frac{n_1{T}_1}{P_1}=\frac{n_2{T}_2}{P_2} \end{gathered}$$

Regards