Analytical Puzzle with Solution
Train Compartment Puzzle
A train has 11 compartments. In any three consecutive compartments, there are exactly 84 people. If there are 321 people in total, how many people are in the 9th compartment?
Solution:
15 people
Explanation :
Let c1,c2,c3……….cn be the compartment in the train
c1 + c2 + c3 + c4 + c5 + c6 + c7 + c8 + c9 + c10 + c11 = 321
In any three consecutive compartments, there are exactly 84 peoples
(c1 + c2+ c3) + (c4 + c5 + c6) + (c7 + c8 + c9) + c10 + c11 = 321
84 + 84 + 84 + c10 + c11 = 321
252 + c10 + c11 = 321
c10 + c11 = 321 – 252
c10 + c11 = 69
Since compartment 9,10,11 are consecutive they will also have 84 peoples
c9 + c10 +c11 = 84
c9 + 69 = 84
c9 = 84 – 69
c9 = 15
Therefore, 15 people are there in the 9th compartment
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