Question

Two types of boxes A, B are to be placed in a truck having a 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 weighs 10 tons i.e. 10000 kg.
So,
$$150x+100y=10000$$
$$\Rightarrow 15x+10y=1000$$
$$\Rightarrow 3x+2y=200.....\left(I\right)$$

 

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.
$$260x+40y=10000$$
$$\Rightarrow 26x+4y=1000$$
$$\Rightarrow 13x+2y=500.....\left(II\right)$$

 

Subtracting (I) from (II) we get

$$13x-3x+2y-2y=500-200$$
$$\Rightarrow 10x=300$$
$$\Rightarrow x=30$$

 

$$\text{ Putting the value of x }=30\text{ in }\left(I\right)$$
$$3\left(30\right)+2y=200$$
$$\Rightarrow 90+2y=200$$
$$\Rightarrow 2y=200-90=110$$
$$\Rightarrow y=\frac{110}{2}=55$$

Thus, weight of box A = 30 kg and that of box B = 55 kg.