Question

Shatabdi express has a capacity of 500 seats of which 10% are in Executive class and the rest being in chair cars. During one journey the train was booked 85% of its capacity. If Executive class was booked to 96% of its capacity, then how many chair car seats were empty during that journey?
${\text{A}}{\text{. 113}}$
${\text{B}}{\text{. 93}}$
${\text{C}}{\text{. 73}}$
${\text{D}}{\text{. 53}}$

Answer 1

Hint: In such types of questions find the number of seats in the executive class by solving the percentage. Then using simple subtraction find seats in the chair car and proceed to solve the question.

Complete step-by-step answer:
We have been given in the question that-
Total number of seats \[ = {\text{ }}500\]
So, as per the question, Number of Executive class seats = 10% of 500 i.e.,
Number of Executive class seats$ = \dfrac{{10}}{{100}} \times 500$
Now, Number of seats in chair cars = total number of seats – number of seats in Executive class
Number of seats in chair cars \[ = {\text{ }}500{\text{ }}-{\text{ }}50\]
Number of seats in chair cars\[\; = {\text{ }}450\]
It is given that during a journey the train was booked 85% of its capacity. So
Number of seats booked in the complete train = 85% of 500
Number of seats booked in the complete train $\dfrac{{85}}{{100}} \times 500 = 85 \times 5 = 425$
It is also given that the Executive class is booked 96% of its capacity. So
Number of seats booked in Executive class = 96% of 50
Number of seats booked in Executive class $\dfrac{{96}}{{100}} \times 50 = \dfrac{{96}}{2} = 48$
Number of chair car seats booked = number of seats booked in the train – number of seats booked in Executive class
Number of chair car seats booked \[ = {\text{ }}425{\text{ }}-{\text{ }}48\]
Number of chair car seats booked \[ = {\text{ }}377\]
So,
Total seats empty in chair car = number of seats in chair car – number of seats booked in chair car
Total seats empty in chair car \[ = {\text{ }}450{\text{ }}-{\text{ }}377{\text{ }} = {\text{ }}73\]
Hence option (C) is correct.

Note: Whenever solving such types of questions, use the basic principle of addition, subtraction and percentage calculation. Always note down the things given in the question to reduce complexity. Step by step solve the equations and reach the answer. As mentioned in the solution first find 10% of the total seats and then proceed with further steps of finding the no. of seats.