Final answer:
The pressure at the larger piston increases by ΔP when the pressure at the smaller piston is increased by ΔP, as per Pascal's principle.
Step-by-step explanation:
When the pressure at the smaller piston in a hydraulic lift is increased by ΔP, the pressure at the larger piston is expected to increase by the same amount, ΔP. This is because in a hydraulic system, according to Pascal's principle, a change in pressure applied to an enclosed fluid is transmitted undiminished to every part of the fluid and to the walls of its container. Therefore, if one piston has an area that is three times the area of the other, the force exerted by the fluid would be greater at the larger piston, but the pressure increase (ΔP) experienced due to the pressure change at the smaller piston stays the same. It does not multiply by the area.