An electric kettle has two thermal coils. When a current is passed in one of them, water in the kettle boils in 6 minutes and when current is passed in other one, the water boils in 8 minutes.

If both the coils are joined in parallel, then how long will it take water to boil ?

3.43 min

Let Power of coils are P₁ and P₂ respectively then 

$R_1= \frac{V^2}{P_1} \text{ and } R_2  = \frac{V^2}{P_2} \text{ respectively.}$

$ t_1 = \frac{H}{P_1}$

$ t_2 = \frac{H}{P_2}$

In Parallel Combination$ P = P_1 + P_2 $

$ t_p = \frac{H}{P} = \frac{H}{P_1 + P_2} = \frac{t_1t_2}{t_1+t_2} =\frac{6\times 8}{6+8}= 3.43min.$