Even if you are sure that the option is misvalued, you can't say that there is arbitrage gain. Why?? because the volatilty you used to price your option is almost sure different from the one used from the other side.
So if you are sure of your volatility, you can buy a variance or a volatility swap/option to make gain of your information.
Regarding your educational case, this three conditions should be satisfied ($P$ is the value of your portfolio):
$$P_0=10-X*200+B=0$$ (B is the amount invested in 1y bond) $$P_T(240)=35-X*240+B(1+r)>0$$ (r is the risk free rate and $P_T$ the portfolio value at maturity if the stock goes up to 240). $$P_T(180)=0-X*180+B(1+r)>0$$ the first equations gives: $$B=200X-10$$ you replace B by its value in the second and the third equations and you will get the condition for your X.