Question & Answer
QUESTION

In Godavari Express, there are as many wagons as there are the number of seats in each wagon and not more than one passenger can have the same berth(seat). If the middlemost compartment carrying 25 passengers is filled with 71.428% of its capacity, then find the maximum number of passengers in the train that can be accommodated if it has a minimum 20% of seats always vacant.
(a) 500
(b) 786
(c) 980
(d) 340

ANSWER Verified Verified
Hint: We are given 71.428% capacity = 25 passengers. Use a unitary method to find the number of passengers in 1% capacity. Multiply this by 100 to find the number of seats in each wagon and the number of wagons. Using these, find the total number of seats. Now, find 80% of these total seats as 20% seats are always vacant. This is your final answer.

Complete step-by-step answer:
In this question, we are given that in Godavari Express, there are as many wagons as there are the number of seats in each wagon and not more than one passenger can have the same berth(seat). The middlemost compartment carrying 25 passengers is filled with 71.428% of its capacity.
We need to find the maximum number of passengers in the train that can be accommodated if it has a minimum of 20% of seats always vacant.
Given, 25 passengers are equal to 71.428% of the total capacity of the wagon.
This means that 71.428% capacity = 25 passengers
So, using the unitary method, we will get the following:
1% capacity = $\dfrac{25}{71.428}$ passengers
Hence, 100% capacity = $\dfrac{25}{71.428}\times 100=35$passengers.
So, the capacity of 1 wagon is 35 passengers.
And, number of wagons = 35.
So, total capacity of train = $35\times 35=1225$ passengers.
But we are given that 20% are always vacant.
So, only 80% seats will be occupied.
Total number of seats that can be occupied = $\dfrac{80}{100}\times 1225=980$
So, the maximum number of passengers in the train that can be accommodated is 980 passengers.
Hence, option (c) is correct.

Note: In this question, it is very important to know about the unitary method. The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value. Also, note that it is given in the question that 20% seats are always vacant. Do not forget to subtract this 20%.