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1. 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

Solution:

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{aligned} \Rightarrow x = (\frac{350 \times 100}{70}) \\ \Rightarrow x = 500 kg \end{aligned}

.
Average weight of four heaviest boxes

\begin{aligned} = (\frac{500 + 350 + 300 + 250}{4}) kg \\ =  350  kg \end{aligned}

Average weight of four lightest boxes

\begin{aligned} = (\frac{200 + 250 + 300 + 350}{4}) kg \\ = 275 kg \end{aligned}

∴ Required difference
= (350 - 275)
= 75 kg

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