  In this work, we have developed an FLRW type model of a universe which
displays transition from deceleration in the past to the acceleration at the
present. For this, we have considered field equations of $f(R,T)$ gravity and
have taken $f(R,T) = R + 2 \lambda T$, $\lambda$ being an arbitrary constant.
We have estimated the $\lambda$ parameter in such a way that the transition red
shift is found similar in the deceleration parameter, pressure and the equation
of state parameter $\omega$. The present value of Hubble parameter is estimated
on the basis of the three types of observational data set: latest compilation
of $46$ Hubble data set, SNe Ia $580$ data sets of distance modulus and $66$
Pantheon data set of apparent magnitude which comprised of 40 SN Ia binned and
26 high redshift data's in the range $0.014 \leq z \leq 2.26 $. These data are
compared with theoretical results through the $ \chi^2 $ statistical test.
Interestingly, the model satisfies all the three weak, strong and dominant
energy conditions. The model fits well with observational findings. We have
discussed some of the physical aspects of the model, in particular the age of
the universe.
