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The present work deals with cosmological solutions in $f(R,T)$ gravity theoryfor perfect fluid with constant equation of state ($\omega$). For a viablecosmological solution $\omega$ is restricted to $\omega<\dfrac{1}{3}$. Alsodepending on the sign of an arbitrary constant one has two possible solutions:a finite universe model and an ever expanding model of the universe. Fieldtheoretic description of the model and possibility of a ghost scalar field hasbeen studied. Also, an equivalence with modified Chaplygin gas has been shown.Finally, from the observational data it has been concluded that this modelrepresents an evolution of the universe from matter dominated phase to presentaccelerating phase.

Analytic Solutions and Observational support: A study of $f(R,T)$ gravity with $f(R,T)=R+h(T)$