## Puzzle of the day: 115

**There are five carton box of different weight. They are weighed in pairs of two with all possibilities. The weights in kgs are 165, 168, 169.5, 171, 172.5, 174, 175.5, 177, 180, and 181.5 . How much does each container weigh?**

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Puzzle Of The Day, Question of the day

**There are five carton box of different weight. They are weighed in pairs of two with all possibilities. The weights in kgs are 165, 168, 169.5, 171, 172.5, 174, 175.5, 177, 180, and 181.5 . How much does each container weigh?**

**Lets assume that the weights of five containers are B1, B2, B3, B4 and B5 kg respectively. Also, B1 ≤ B2 ≤ B3 ≤ B4 ≤ B5. It is given that five cartons of oil are weighed two at a time in all possible ways. It means that each of the container is weighted four times. Thus,**

**4×(B1 + B2 + B3 + B4 + B5) = (165 + 168 + 169.5 + 171 + 172.5 + 174 + 175.5 + 177 + 180 + 181.5)**

**4×(B1 + B2 + B3 + B4 + B5) = 1734**

**(B1 + B2 + B3 + B4 + B5) = 433.5 kg……….(1)**

**Now, B1 and B2 must add to 165 as they are the lightest one.**

**B1 + B2 = 165……………(2)**

**Similarly, B4 and B5 must add to 181.5 as they are the heaviest one.**

**B4 + B5 = 181.5………….(3)**

**From above three equation, we get B3 = 87 kg**

**Also, it is obvious that B1 and B3 will add to 168 – the next possible higher value. Similarly, B3 and B5 will add to 180 – the next possible lower value.**

**B1 + B3 = 168………….(4)**

**B3 + B5 = 180………….(5)**

**Substituting B3 = 87, we get B1 = 81 and B5 = 93**

**From 2 & 3 equations, we get B2 = 84 and B4 = 88.5**

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

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