Question

There are 10 compartments in passenger train carries on average 15 passengers per compartment. If at least 15 passengers were sitting in each compartment, no compartment has an equal number of passengers, and any compartment does not exceed the number of average passengers except the $ {{10}^{th}} $ compartment. Find how many passengers can be accommodated in the $ {{10}^{th}} $ compartment.

Answer 1

Hint: The maximum passengers in all the compartments except the $ {{10}^{th}} $ compartment will be 15. We will take the number of passengers in the first compartment as 15 and the number of passengers will be decreasing in each compartment as no two compartments have equal number of passengers, so we will decrease the number of passengers by 1 in each consecutive compartment up to 15 compartment, leaving 10 compartment. We will get the number of passengers in the 10th compartment by subtracting the sum of passengers in all 14 compartments from the total number of passengers, that is, 150.

Complete step-by-step answer:
It is given in the question that there are 10 compartments in passenger trains carrying on average 15 passengers per compartment. If at least 15 passengers were sitting in each compartment, no any compartment has equal number of passengers, and any compartment does not exceed the number of average passengers except the $ {{10}^{th}} $ compartment and we have been asked to find how many passengers can be accommodated in $ {{10}^{th}} $ compartment.
So, there are 10 compartments in the passenger train, hence the total number of passengers will be,
 $ \text{No}\text{. of compartments }\!\!\times\!\!\text{ Average passengers} $
We know that the number of compartments is 10 and we have also been given that the average passengers is 15. So, we can write the total number of passengers as,
 $ 10\times 15=150 $
Now, as we know that no two compartments can have the same number of passengers, so the passengers can be arranged as,
 $ 15+14+13+12+11+10+9+8+7 $
And its sum is 99.
We know that there a total of 150 passengers, so the number of passengers in the $ {{10}^{th}} $ compartment will be,
(Total number of passengers) – (99)
= 150 – 99
= 51
Thus, there will be 51 passengers in the $ {{10}^{th}} $ compartment of the passenger train.

Note: Most of the students skip the line, no any compartment has equal number of passengers and as a result they add 15 passengers in each compartment and when they find the number of passengers in the $ {{10}^{th}} $ compartment, they will get, 150 – 135 = 15 passengers and this is wrong. So, it is recommended that the students read and understand the question carefully.