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.