In Sabarmati Express, there are as many wagons as 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 no. of passengers in train that can be accommodated if it has minimum 20% seats always vacant.
(a) 500
(b) 786
(c) 980
(d) Can’t be determined
Ans: (c) 980
Explanation:
No of wagon = No of seats in each wagon
We know, \displaystyle\frac{1}{14} = 7.1428\%
\qquad \Rightarrow71.428\% = \displaystyle\frac{10}{14} = \displaystyle\frac{5}{7}
71.428\% = \displaystyle\frac{5}{7} \Rightarrow This means 5 seat is filled for every 7 seats capacity
Now, \displaystyle\frac{5}{7} = \displaystyle\frac{25}{35}
Hence, wagon = seat = 35
The seat is always 20% vacant.
So, it can carry maximum 80% passengers.
Hence, maximum passenger
= 35\times 35\times \displaystyle\frac{25}{35}
= 980
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How do you you find number of wagon = 35
If 5 seat if filled, seat capacity = 7
So, 25 seat filled = 35 seat capacity
Just do the simple unitary, and you will get the answer.
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