Answer
No.
Work Step by Step
The two substances' densities change with temperature at different rates, therefore the thermometers would reach the $60^{\circ}C$ measurement at different real temperatures.
P.S. If the alcohol that the problem refers to is ethanol, and the pressure inside the thermometer is 1 atm, at $100 ^{\circ}C$ it would be a vapor (b.p.$ 78 ^{\circ}C$), making it more clear that dividing the scale in 100 equal parts would yield inaccurate measurements.
