The Malefic Milkman

Standard selling rate of milk = (35+42)/14= £5.5 per Kg but milk man wanted to profit £78 so total 78+35=£113 will be earned by selling milk. So dark matter will be needed => 5.5X = (78+35) + 1*(X-14) [ let X= total amount of product i.e. milk plus dark matter ] then we get X= 22 Kg so amount of dark matter that milkman needed to add with milk is (22-14=8 Kg) Ans: 8 Kg.

Before adding any dark matter, the Malefic Milkman, (MM), would have sold the $14$ kg of powdered milk for $£35 + £42 = £77,$ which works out to $\dfrac{£77}{14 kg} = \dfrac{11}{2}$ £/kg..

By adding $x$ kg of dark matter at $£1$ per kg., MM would then have $(14 + x)$ kg of product at a cost of $£(35 + x),$ from which he wants to make a profit of $£78.$ Since he still plans to sell the product at a price of $\dfrac{11}{2}$ £/kg, and since the cost to him of the product is $\dfrac{(35 + x)}{14 + x}$ £/kg, he will need to add $x$ kg of dark matter such that

$(14 + x)\left(\dfrac{11}{2} - \dfrac{(35 + x)}{14 + x}\right) = 78 \Longrightarrow 77 + \dfrac{11}{2}x - (35 + x) = 78 \Longrightarrow \dfrac{9}{2}x = 36 \Longrightarrow x = 8$ kg.

So in order for MM to make a profit of $£78$ he will to add $\boxed{8}$ kg of dark matter.