# Application Problems

In everyday life we heard about the fact that global rise in fuel prices leads to petrol price like. If less petrol is consumed then the bill amount will be less. This means that one quantity affects the another. Petrol bill depends upon the quantity of petrol consumed. We say that the quantity of petrol is an independent variable and the amount of petrol bill is the dependent variable. The relation between such variables can be shown through graph.

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**Example :** (Quantity and cost)

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The following table gives the quantity of Rice and its cost

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Number of kgs of Rice |
10 | 15 | 20 | 25 |

Cost of Rice (in Rs) |
300 | 450 | 600 | 750 |

Plot a graph to show the data

(i) Mark the number of kgs of Rice in *x*- axis (horizontal axis) with 1 unit = 5 kgs

(ii)Mark the cost of Rice in *y*-axis (vertical axis) with 1 unit = Rs. 100

(iii) Plot the points (10, 300), (15, 450), (20, 600), (25, 750)

(iv) Join the points.

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The graph pass through the origin. Suppose we want to know the price of 17 kgs of Rice. Locate 17 on horizontal axis, then follow the vertical line through 17 till you meet the graph at P. From P you take a horizontal line to meet the vertical axis at 475. This meeting (17, 475) point provides the answer. This is a graph of situation in which two quantities are in direct variation. The graph will always be linear.

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(Principal and simple Interest)

A bank gives 11% simple interest on deposits by senior citizens. Draw a graph to illustrate the relation between the sum deposited and simple interest earned. Find from your graph.

(i) the annual interest obtainable for an investment of Rs. 500.

(ii) the investment one has to make to get an annual simple interest of Rs. 88.

Sum deposited |
Simple Interest for a year |

Rs. 500 | |

Rs. 600 | |

Rs. 700 | |

Rs. 800 | |

Rs. 900 | |

Rs. 1000 |

Deposit (Rs) |
500 | 600 | 700 | 800 | 900 | 1000 |

Annual S.I (in Rs) |
55 | 66 | 77 | 88 | 99 | 110 |

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(a) Mark the deposit in Rs. on *x*- axis (horizontal axis) with 1 unit = Rs. 100

(b) Mark Annual simple interest in Rs. on *y*-axis (vertical axis) with 1 unit = Rs. 10

(c) Plot the points (500, 55), (600, 66), (700, 77), (800, 88), (900, 99), (1000, 110)

(d) Join the points.

We get a graph that is linear.

(i) For Rs. 500 on *x*-axis, we get interest to be Rs. 55 on *y*-axis.

(ii) For Rs. 88 on *y*-axis, we get the deposited amount Rs. 800 on *x*-axis.

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(Time and Distance)

Â Akshay can ride a car constantly at a speed of 40 kms/ hour. Draw time-distance graph for Â this situation. Use it to find.

(i) time taken by Akshay to cover 160 km.

(ii) the distance covered by Akshay in hrs.

Hours of ride |
Distance Covered |

1 hrs | 40kms |

2 hrs | 2 Ã— 40 = 80 km |

3 hrs | 3 Ã— 40 = 120 km |

4 hrs | 4 Ã— 40 = 160 km |

5 hrs | 5 Ã— 40 = 200 km |

We get the table of values

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Time |
1 | 2 | 3 | 4 | 5 |

Distance covered (in km) |
40 | 80 | 120 | 160 | 200 |

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Scale: *x*-axis 1 units = 1 hour

*y*-axis 1 unit = 40 kms

(a) Mark time on horizontal axis

(b) Mark distance on vertical axis

(c) Plot the points (1, 40), (2, 80), (3, 120), (4, 160), (5, 200).

(d) Join the points. We get a linear graph.

(i) In vertical axis 160km corresponds to 4 hrs in horizontal axis.

(ii) In horizontal axis has corresponds to 100km in vertical axis.\

Akshay covers 160 km in 4 hrs and in hrs he is able to cover a distance of 100 km.