Some Applications
In many scenarios, we have observed that there are existing relations between quantities/variables. For example: If we use more electricity, the electricity bill amount is more. If we reduce our groceries, the daily expense of our household is lower.
These are all instances where one quantity/variable affects another. For such cases, we try to identify the independent and dependent variable.
In the case for the electricity consumption and the amount due on the bill, we can say that the quantity of electricity used is an independent variable (also called control variable) and the amount of electric bill is the dependent variable. The relation between such variables can be shown by plotting recorded dat points on a graph.
- The following table contains the data regarding the interest on a number of deposits for a year:
| Deposit (Rs) | Simple Interest (Rs) |
|---|---|
| 1000 | 80 |
| 2000 | 160 |
| 3000 | 240 |
| 4000 | 320 |
| 5000 | 400 |
Plot the graph and answer the below questions.
(a) Does the graph pass through the origin?
(b) Find the interest on Rs.2500 for a year: Rs.
(c) To get an interest of Rs.280 per year, how much money should be deposited? Rs.
Join the coloured data points with straight lines.
Solution:
(a) From the graph, we can observe that the line will pass through the origin. We can also approach this question logically by asking- if we deposit Rs.0 (no money at all), what will be the simple interest on it? The answer will be also zero. Thus, the point (0,0) satisfies the relation.
(b) Using the point (2000,160) and (3000, 240) we can interpolate for the value x = 2500. Let the simple interest on Rs.2500 be a. We get:
a - 160 = 40
a = Rs. 200
(c) Similarly, like in (b), we now have the value y = 280 and we need to find the corresponding x value. Let the amount to be deposited be b. Using interpolation between the points (3000,240) and (4000,320):
4000 - b = 500
b = Rs. 3500
Answer: The number of litres of petrol you buy to fill a car’s petrol tank will decide the amount you have to pay. Which is the independent variable here?
Solution: Since, the more amount of petrol we buy, the more amount of money we will have to pay. Thus, the amount of petrol purchased in the independent variable while the money due for payment is dependent variable.
Let's Solve
The following table gives the quantity of petrol and its cost. Plot the graph for the data points.
| No. of Litres of petrol | Cost (Rs) |
|---|---|
| 10 | 500 |
| 15 | 750 |
| 20 | 1000 |
| 25 | 1250 |
Join the coloured data points with straight lines.
A bank gives 10% Simple Interest (S.I.) on deposits by senior citizens. Draw a graph to illustrate the relation between the sum deposited and simple interest earned. Also find from the graph:
(a) the annual interest obtainable for an investment of Rs 250 Rs.
(b) the investment one has to make to get an annual simple interest of Rs 70 Rs.
Use the data points for 'sum deposited' equal to Rs.100 , Rs.200, Rs.300, Rs.400, Rs.500 and Rs.1000.
Use the formula:
Simple Interest =
where,
P - principal amount
R - rate of interest
T - time period
Join the coloured data points with straight lines.
| Sum deposited (Rs) | SI Calculation | Simple interest (1 year) (Rs) |
|---|---|---|
| 100 | 10 | |
| 200 | 20 | |
| 300 | 30 | |
| 400 | 40 | |
| 500 | 50 | |
| 1000 | 100 |
(a) From the drawn graph, we can conclude that for the amount of Rs 250 deposited we will get an interest of Rs 25.
(b) From the drawn graph, we can conclude that for an interest of Rs 70, we need to deposit an amount of Rs. 700.
Ajit can ride a scooter constantly at a speed of 30 kms/hour. Draw a time-distance graph for this situation. Use the graph to find:
(i) the time taken by Ajit to ride 75 km
(ii) the distance covered by Ajit in 3
Use the data points for time equal to 1 hour, 2 hours, 3 hours and 4 hours.
| Hours of ride (hr) | Distance covered (km) |
|---|---|
| 1 | 30 |
| 2 | 60 |
| 3 | 90 |
| 4 | 120 |
Join the coloured data points with straight lines.
(i) From the drawn graph, we can conclude that for covering 75 km, we need 2.5 hours to cover the distance.
(ii) From the drawn graph, we can conclude that in 3
Draw the graph for the following tables and answer (Yes/No) if the graph obtained is linear:
(a) Side of square and corresponding perimeter:
| Side of square(cm) | Perimeter (cm) |
|---|---|
| 2 | 8 |
| 3 | 12 |
| 3.5 | 14 |
| 5 | 20 |
| 6 | 24 |
Join the coloured data points with straight lines.
Is it linear?
(b) Side of square and corresponding area:
| Side of square(cm) | Area (cm2) |
|---|---|
| 2 | 4 |
| 3 | 9 |
| 4 | 16 |
| 5 | 25 |
| 6 | 36 |
Join the coloured data points with straight lines.
Is it linear?