Question

Following are the car parking charges near a railway station up to: $4\mathrm{hours}\mathrm{Rs}.60,8\mathrm{hours}\mathrm{Rs}.100,12\mathrm{hours}\mathrm{Rs}.140,24\mathrm{hours}\mathrm{Rs}.180.$ Check is the parking charges are in direct proportional to the parking time.

Answer 1

Step 1. Finding the charges per hour when rate is $\mathrm{Rs}.60$ for $4\mathrm{hour}$

For $4\mathrm{hour}$ the car is charged $\mathrm{Rs}.60$

Let the charge for $1\mathrm{hour}$ is $C_1$

Therefore,

$$\begin{gathered} C_1=\frac{60}{4} \\ =15 \end{gathered}$$

$\therefore$The charge per $\mathrm{Hour}$ is $\mathrm{Rs}.15$

Step 2. Finding the charges per hour when rate is $\mathrm{Rs}.100$ for $8\mathrm{hour}$

For $8\mathrm{hour}$ the car is charged $\mathrm{Rs}.100$

Let the charge for $1\mathrm{hour}$ is $C_2$

Therefore,

$$\begin{gathered} C_2=\frac{100}{8} \\ =12.5 \end{gathered}$$

The charge per $\mathrm{Hour}$ is $\mathrm{Rs}.12.5$

Step 3. Finding the charges per hour when rate is $\mathrm{Rs}.140$ for $12\mathrm{hour}$

For $12\mathrm{hour}$ the car is charged $\mathrm{Rs}.140$

Let the charge for $1\mathrm{hour}$ is $C_3$

Therefore,

$$\begin{gathered} C_3=\frac{140}{12} \\ =11.67 \end{gathered}$$

The charge per $\mathrm{Hour}$ is $\mathrm{Rs}.11.67$

Step 4. Finding the charges per hour when rate is $\mathrm{Rs}.180$ for $24\mathrm{hour}$

For $24\mathrm{hour}$ the car is charged $\mathrm{Rs}.180$

Let the charge for $1\mathrm{hour}$ is $C_4$

Therefore,

$$\begin{gathered} C_4=\frac{180}{24} \\ =7.50 \end{gathered}$$

The charge per $\mathrm{Hour}$ is $\mathrm{Rs}.7.50$

Step 5. Finding the proportion.

The charges per hour are not the same that is, $C_1\ne C_2\ne C_3\ne C_4$

Hence, the parking charges are not in direct proportion to the parking time.