We employed metadynamics-based classical molecular dynamics simulations to methylated adenine-thymine (mA-mT) and guanine-cytosine (mG-mC) base pairs to see favorable conformations in various concentrations of hydrated 1-ethyl, 3-methyl imidazolium acetate. We investigated various stacked and hydrogen-bonded conformations of association of base pairs through appropriately chosen collective variables. Stacked conformations more favored in water for both base pairs, whereas Watson-Crick (WC) hydrogen-bonding conformations are favored in pure and hydrated ionic liquids (ILs) except for 0.75 mol fraction IL. We observe that EMIm cations surround the base pairs in WC conformations creating a kind of hydrophobic cavity and protect the hydrogen bonds between base pairs. However, the five-membered heteroaromatic rings of cations stack with the nucleobases in the cation-base-cation (pi -pi-pi) model, which resembles the base-base-base stacking in a DNA duplex. Interestingly, from additional simulations of 0.5 mol fraction hydrated choline dihydrogen phosphate IL, we observe that the stacked conformations become more favored than the WC conformation due to the absence of pi-bonds in cations. The calculated values of relative solubility of base pairs in pure and hydrated ionic liquids compared to those in pure water correlate well with the free energy values of WC and stacked conformations.