Question

Two types of boxes A, B are to be placed in a truck having capacity of 10 tons. When 150 boxes of type A and 100 boxes of type B are loaded in the truck, it weighes 10 tons. But when 260 boxes of type A are loaded in the truck, it can still accommodate 40 boxes of type B, so that it is fully loaded. Find the weight of each type of box.

Answer 1

Let the weight of box A be x and that of box B be y.
When 150 boxes of type A and 100 boxes of type B are loaded in the truck, it weighes 10 tons i.e 10000 kg.
So,
$$\begin{gathered} 150x+100y=10000 \\ \Rightarrow 15x+10y=1000 \\ \Rightarrow 3x+2y=200.....\left(\mathrm{I}\right) \end{gathered}$$
When 260 boxes of type A are loaded in the truck, it can still accommodate 40 boxes of type B, so that it is fully loaded.
$$\begin{gathered} 260x+40y=10000 \\ \Rightarrow 26x+4y=1000 \\ \Rightarrow 13x+2y=500.....\left(\mathrm{II}\right) \end{gathered}$$
Subtracting (I) from (II) we get
$$\begin{gathered} 13x-3x+2y-2y=500-200 \\ \Rightarrow 10x=300 \\ \Rightarrow x=30 \\ \mathrm{Putting}\mathrm{the}\mathrm{value}\mathrm{of}x=30\mathrm{in}\left(\mathrm{I}\right) \\ 3\left(30\right)+2y=200 \\ \Rightarrow 90+2y=200 \\ \Rightarrow 2y=200-90=110 \\ \Rightarrow y=\frac{110}{2}=55 \end{gathered}$$
Thus, weight of box A = 30 kg and that of box B = 55 kg.