To calculate delta, we can find the delta-hedged portfolio, consisting of long $\Delta$ stocks and short a call option. This portfolio should remain the same price in both scenarios of the stock going up to £150 or the stock going down to £75. $$ P = \Delta S - C $$ At expiry, if the stock goes up to £150 then the option payoff is £50. If the stock does down to £75 then the option expires out of the money. Constructing the portfolio for both of these outcomes and setting them to be equal gives $$ \Delta 150 - 50 = 75 \Delta $$ and solving this equation gives us the solution $$ \Delta = \frac{2}{3}. $$