Question

Following are the car parking charges near a railway station up to
$
  \underline {{\text{Time Parking charges}}} \\
  \underline {4{\text{ hours 60 Rs}}{\text{. }}} \\
  \underline {{\text{8 hours 100 Rs}}{\text{. }}} \\
  \underline {{\text{12 hours 140 Rs}}{\text{. }}} \\
  \underline {4{\text{ hours 180 Rs}}{\text{. }}} \\
 $
Check if the parking charges are in direct proportion to the parking time.

Answer 1

Hint: In this question car parking charges are being given and we need to tell if the car parking charges are in direct proportion or not. Now direct proportion refers to the variation in the relation between two quantities where the ratio of the two is equal to a constant value. Use this definition of direct proportion to decode that the ratio of parking charges and number of hours are the same then the parking charges are in direct proportion to the parking time and if not then the parking charges are not in direct proportion to the parking time.

Complete step-by-step answer:
Given time and parking charges are
$
  \underline {{\text{Time Parking charges}}} \\
  \underline {4{\text{ hours 60 Rs}}{\text{. }}} \\
  \underline {{\text{8 hours 100 Rs}}{\text{. }}} \\
  \underline {{\text{12 hours 140 Rs}}{\text{. }}} \\
  \underline {4{\text{ hours 180 Rs}}{\text{. }}} \\
 $
Now if the ratio of parking charges and number of hours are the same then the parking charges are in direct proportion to the parking time and if not then the parking charges are not in direct proportion to the parking time.
So, calculate the ratios we have
$\left( i \right)\dfrac{{{\text{Parking charge}}}}{{{\text{Number of hours}}}} = \dfrac{{60}}{4} = 15{\text{ Rs/hr}}{\text{.}}$
$\left( {ii} \right)\dfrac{{{\text{Parking charge}}}}{{{\text{Number of hours}}}} = \dfrac{{100}}{8} = \dfrac{{25}}{2}{\text{ Rs/hr}}{\text{.}}$
$\left( {iii} \right)\dfrac{{{\text{Parking charge}}}}{{{\text{Number of hours}}}} = \dfrac{{140}}{{12}} = \dfrac{{35}}{3}{\text{ Rs/hr}}{\text{.}}$
$\left( {iv} \right)\dfrac{{{\text{Parking charge}}}}{{{\text{Number of hours}}}} = \dfrac{{180}}{4} = 45{\text{ Rs/hr}}{\text{.}}$
So, as we see that the ratio of parking charges and number of hours is not the same, the parking charges are not in direct proportion to the parking time.
So, this is the required answer.

Note: Whenever we face such types of problems the key concept is to have the basic understanding of the definition of direct proportion. This concept will help in getting the desired relation between the two quantities and figuring out whether they are in direct proportion or not. Use this concept to reach answers to the related problem statements.