three resistance of 20 ohm, 40 ohm, and 60 ohm are connected (1)in series (2)in parallel find their resultant resistance in each case

Dear Student,
​​​​​​Answer to your question is given below:
Given, the three resistances are R₁ = 20 Ω, R₂ = 40 Ω and R₃ = 60 Ω
(i) In series, the resultant resistance is, R_s = R₁ + R₂ + R₃   
                                                                    = (20 + 40 + 60) Ω
                                                                    = 120 Ω
(ii) In parallel, the resultant resistance is given by,
                                                                $$\begin{gathered} \frac{1}{R_p} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} \\ \Rightarrow \frac{1}{R_p} = \frac{1}{20} + \frac{1}{40} + \frac{1}{60} \\ \Rightarrow \frac{1}{R_p} = \frac{6+3+2}{120 } \\ \Rightarrow R_p = \frac{120}{11 }\Omega \\ \Rightarrow R_p = 10.9 \Omega \end{gathered}$$

Regards,