The possibility of the appearance of ∆(1232) isobars in neutron star matter and the so called ∆ puzzle is investigated in a relativistic quark model where the confining interaction for quarks inside a baryon is represented by a phenomenological average potential in an equally mixed scalar-vector harmonic form. The hadron-hadron interaction in nuclear matter is then realized by introducing additional quark couplings to σ, ω, and ρ mesons through mean-field approximations. The hyperon couplings are fixed from the hyperon optical potentials at saturation density. Effects of moderate variations in the ∆-ω and ∆-ρ coupling strength on the critical density of forming ∆ resonances and on the mass-radius relation of neutron stars is studied. We have also made an attempt to study the impact of in-medium mass variations of the ∆ baryon on the structure of neutron stars. It is observed that within the constraints of the mass of the precisely measured massive pulsars, PSR J0348+0432 and PSR J1614-2230, neutron stars with a composition of both ∆ isobars and hyperons is possible in the present model.

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