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?
Check if you were right - full answer with solution below.
Solution:
Let c1,c2,c3.......... cn be the compartment in the train
c1 + c2 + c3 + c4 + c5 + c6 + c7 + c8 + c9 + c10 + c11 = 321In any three consecutive compartments, there are exactly 84 peoples
(c1 + c2 + c3) + (c4 + c5 + c6) + (c7 + c8 + c9) + c10 + c11 = 32184 + 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
