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Context. Class II methanol masers at 6.7 and 12.2GHz occur close to high-mass young stellar objects (HMYSOs). When they are observed simultaneously, such studies may contribute to refining the characterisation of local physical conditions.
Aims. We aim to search for the 12.2GHz methanol emission in 6.7GHz methanol masers that might have gone undetected in previous surveys of northern sky HMYSOs, mainly due to their variability. Contemporaneous observations of both transitions are used to refine the flux density ratio and examine the physical parameters.
Methods. We observed a sample of 153 sites of 6.7GHz methanol maser emission in the 12.2GHz methanol line with the Torun 32m radio telescope, using the newly built X-band receiver.
Results. The 12.2GHz methanol maser emission was detected in 36 HMYSOs, with 4 of them detected for the first time. The 6.7-12.2GHz flux density ratio for spectral features of the contemporaneously observed sources has a median value of 5.1, which is in agreement with earlier reports. The ratio differs significantly among the sources and for the periodic source G107.298+5.639 specifically, the ratio is weakly recurrent from cycle to cycle, but it generally reaches a minimum around the flare peak. This is consistent with the stochastic maser process, where small variations in the physical parameters along the maser path can significantly affect the ratio. A comparison of our data with historical results (from about ten years ago) implies significant (>50%) variability for about 47 and 14% at 12.2 and 6.7GHz, respectively. This difference can be explained via the standard model of methanol masers.