One filament takes 10 min to heat a kettle and another takes 15 min. If connected in parallel, they combindly take ______ min to heat the same kettle.

Lets suppose E energy is required to heat the kettle and P1 and P2 are the power of filament which take 10 min and 15 min respectively to heat the kettle. So P1=E10 and P2=E15. Now both the filaments are connected in parallel to heat the same kettle hence their combined power will be (P1 + P2) but the energy required is still E. If the time they take is t then P1+P2t=E⇒E10+E15t=E ⇒5E30×t=E⇒t=6min