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?

Train Compartment Puzzle

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