An electric kettle has two coils. When one of these is switched on , the water in the kettle boils in 6 min. When the other coil is switched on, the water boils in 3 min. If the two coils are connected in series, what is the time taken to boil the water in the kettle?

9 min

$\text{Let amount of heat required to boil water is H}$

$ P_1 = \frac{V^2}{R_1} =\frac{H}{t_1} , P_2 = \frac{V^2}{R_2} =\frac{H}{t_2}$

$\text{ In Series }P = \frac{V^2}{R_1+R_2} = \frac{P_1P_2}{P_1+P_2}$

$ t = \frac{H}{P} = \frac{H}{P_1} +\frac{H}{P_2} = t_1 +t_2 = 9 min$