### There are five boxes in a cargo hold. The weight of the first box is 200 kg and the weight of the second box is 20% more than the weight of third box, whose weight is 25% more than the first box’s weight. The fourth box at 350 kg is 30% lighter than the fifth box. The difference in the average weight of the four heaviest boxes and the four lightest boxes is.

A. 37.5 kg

B. 51.5 kg

C. 75 kg

D. 112.5 kg

Weight of first box = 200 kg Weight of third box = 125 % of 200 kg = 250 kg Weight of second box = 120% of 250 kg = 300 kg Weight of fourth box = 350 kg Let the weight of fifth box be x kg Then, 70% of x = 350 kg $\begin{array}{l} \Rightarrow x=\left(\Large\frac{350 \times 100}{70}\right) \\ \Rightarrow x=500 \mathrm{~kg} \end{array}$ Average weight of four heaviest boxes $\begin{array}{l} =\left(\Large\frac{500+350+300+250}{4}\right) \mathrm{kg} \\ =350 \mathrm{~kg} \end{array}$ Average weight of four lightest boxes $\begin{array}{l} =\left(\Large\frac{200+250+300+350}{4}\right) \mathrm{kg} \\ =275 \mathrm{~kg} \end{array}$ $\begin{array}{l}\text{∴ Required difference}\\ \text{= (350 – 275)}\\ \text{= 75 kg}\end{array}$