Delhi to Bangalore Rajdhani Express when departed had 200 people travelling in it. There were 20 stations numbered 1 through 20, excluding the source station. At every station which is a multiple of 3, 20 people joined the train. At every station which is a multiple of 7, 30 people entered the train. At every remaining odd-numbered station, 20 people left the train. At every remaining station, 10 people left the train.
How many unique people travelled via train?
Answers
Given,
Total stations = 20 [1 - 20]
Total people who travelled = 200 people
At every station which is a multiple of 3, 20 people joined the train
At every station which is a multiple of 7, 30 people entered the train
At every remaining odd-numbered station, 20 people left the train
At every remaining station, 10 people left the train
To Find,
The number of unique people traveled via train =?
Solution,
The stations are numbered as follow:
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20
The multiples of 3 = 3,6,9,12,15,18
The number of station which ar emultiple of 3 = 6
The number of people joined train at station which is multiple of 3 = 20
The total number of people who joined train at the station which is a multiple of 3 = 20 * 6 = 120 people
The multiples of 7 = 7,14
The total number of people who joined train at the station which is a multiple of 7 = 2 * 30 = 60 people
The remaining odd stations = 1,5,11,13,17,19
The total number of people who left the train a from the remaining odd-numbered stations = 6 * 20 = 120 people left the train
The remaining station = 2,4,8,10,16,20
The total number of people who left the train a from the remaining stations = 6 * 10 = 60 people left the train
The total people who travelled train = 200 + 120 +60 - 120 - 60 = 200 people
Total unique people who travelled via train = 200 + 120 + 60 = 380
Hence, the number of unique people traveled via train is 380