Weight Calculation of Each Container

What was the given data?

Let's name five containers as C1, C2, C3, C4 and C5 with their increasing order of weights. That is weight of C1 <= C2 <= C3 <= C4 <= C5.


As per given data, weight of these containers when weighed in pairs -

165, 168, 169.5, 171, 172.5, 174, 175.5, 177, 180, and 181.5 . Here, weights too are in the increasing order.

It's quite obvious that the the container having lowest weight and the second lowest weight will weigh lowest in all possible pairs.That is 165 kg must be weight of pair C1-C2.

C1 + C2 = 165  

And the next higher pair weight of 168 kg must be involving lowest weighing container C1 and third lowest weighing container C3.

C1 + C3 = 168

Similarly, C4 and C5 together must weigh highest when weighed in pair.

C4 + C5 = 181.5

And same way, C3 and C5 makes second highest weighing pair.

C3 + C5 = 180.

It's quite clear that each of the container is weighed 4 times as each of them appearing in 4 pairs.

So, if weight all above pairs are added then, 

4 ( C1 + C2 + C3 + C4 + C5 ) = 165+168+169.5+171+172.5+174+175.5+177+180+181.5= 1734 kg


( C1 + C2 + C3 + C4 + C5 ) = 433.5 kg     .......(1)

Putting C1 + C2 = 165 and C4 + C5 = 181.5 in above,

165 + C3 + 181.5 = 433.5 

C3 = 87 kg.

Since, C1 + C3 = 168, 

C1 = 168 - 87

C1 = 81 kg.

Also, we have, C3 + C5 = 180

C5 = 180 - 87

C5 = 93 kg.

Since, C4 + C5 =  181.5 

C4 = 181.5 - 93 = 88.5 kg. 

Again, C1 + C2 =  165

C2 = 165 - 81 = 84 kg.

Hence, the weights of five containers are 81, 84, 87, 88.5 and 93 kg.