To answer the given question comprehensively, let's break down the steps required to find the solution to each part:
(i) Finding the time spent by Varun in the mall:
1. Fixed parking charge for cars: Rs. 50
2. Hourly parking rate for cars: Rs. 20 per hour
3. Total amount paid by Varun for parking his car: Rs. 30
Given that Varun paid Rs. 30 for parking, we need to find out how much time he spent in the mall.
The hourly parking charge for the car is Rs. 20 per hour. The total parking charge (excluding the fixed charge) that Varun paid is equal to the time spent in hours multiplied by the hourly rate.
[tex]\[
\text{Total parking charge} = \text{Hourly rate} \times \text{Time spent in hours}
\][/tex]
Based on the given information:
[tex]\[
30 = 20 \times \text{Time spent}
\][/tex]
Solving the above equation:
[tex]\[
\text{Time spent} = \frac{30}{20} = 1.5 \text{ hours}
\][/tex]
Therefore, Varun spent 1.5 hours in the mall.
(ii) Finding the difference in the amount paid if Varun came by scooter:
1. Fixed parking charge for scooters: Rs. 20
2. Hourly parking rate for scooters: Rs. 10 per hour
3. Time spent in the mall (calculated from part (i)): 1.5 hours
Now, we need to calculate the total parking charge Varun would have paid if he came by scooter.
[tex]\[
\text{Total parking charge for scooter} = \text{Fixed charge for scooter} + (\text{Hourly rate for scooter} \times \text{Time spent in hours})
\][/tex]
Plugging in the values:
[tex]\[
\text{Total parking charge for scooter} = 20 + (10 \times 1.5) = 20 + 15 = 35 \text{ rupees}
\][/tex]
Next, calculate the difference in the amount paid:
1. Total amount paid if Varun came by car: Fixed charge for car + Total parking charge for car
[tex]\[
\text{Total amount paid by car} = 50 + 30 = 80 \text{ rupees}
\][/tex]
2. Total amount paid if Varun came by scooter: 35 rupees (as calculated above)
[tex]\[
\text{Difference in amount paid} = \text{Total amount paid by car} - \text{Total amount paid by scooter} = 80 - 35 = 45 \text{ rupees}
\][/tex]
Hence, the difference in the amount paid by Varun if he would have come by scooter instead of car is 45 rupees.
To summarize:
- The time spent by Varun in the mall is 1.5 hours.
- The difference in the amount paid by Varun if he would have come by scooter instead of car is 45 rupees.
