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A mixture of two gases A and B in the mole ratio 2 : 3 is kept in a 2 litre vessel. A second 3 litre vesselhas the same two gases in the mole ratio 3 : 5. Both gas mixtures have the same temperature and same total pressure. They are allowed to intermix the final temperature and total pressure are the same as the initial values, the final volume being 5 litres. Given that the molar masses are MB and MB, what is the mean molar mass of the final mixture?

(1) $\frac{77{M}_{A} + 123{M}_{B}}{200}$

(2) $\frac{123{M}_{A} + 77{M}_{B}}{200}$

(3) $\frac{77{M}_{A} + 123{M}_{B}}{250}$

(4) $\frac{{\text{123M}}_{\text{A}}\text{\hspace{0.17em}}+\text{\hspace{0.17em}}77{\text{M}}_{\text{B}}}{250}$