- Introduction
- Direct Proportion
- How to Solve Direct Proportion Problems
- Inverse proportion
- How to Solve Inverse Proportion Problems

For example:

(i) As the speed of a vehicle increases, the time taken to cover the same distance decreases

(ii) More apples cost more money

(iii) More interest earned for more money deposited.

(iv) More distance to travel, more petrol needed.

if they increase (decrease) together in such a manner that the ratio of their corresponding values remains constant.

That is if

Then

$\frac {x_1}{y_1}= \frac {x_2}{y_2}$

(1) We know that in direct Proportion

$\frac {x_1}{y_1}= \frac {x_2}{y_2}=\frac {x_3}{y_3} =\frac {x_n}{y_n}$

In a problem, one ratio would be given. So using the above equation, we can easily find the unknown terms

The cost of 5 kg of a particular quality of sugar is Rs 200. Tabulate the cost of 1,2, 4, 10 and 14 kg of sugar of the same type

Let x kg of sugar cost y rupees

x |
1 |
2 |
4 |
5 |
10 |
14 |

y |
? |
? |
? |
200 |
? |
? |

As the number of kg increases, cost of the sugar also increases in the same ratio. It is

Now let’s use the above expression

$\frac {x_1}{y_1}= \frac {x_2}{y_2}=\frac {x_3}{y_3} =\frac {x_n}{y_n}$

Now we have

(a)

$\frac {x_4}{y_4} = \frac {5}{200}$

$ \frac {1}{y} = \frac {5}{200}$

y=Rs 40

(b)

$\frac {x_2}{y_2} = \frac {x_4}{y_4}

2/y = 5/200

y=Rs 80

Similarly, other can be found

Complete table would be

x |
1 |
2 |
4 |
5 |
10 |
14 |

y |
40 |
80 |
160 |
200 |
400 |
560 |

(2) We know that in direct Proportion

$ \frac {x}{y}= k$

$x=ky$

So we can find value of k from known values, and then use the formula to calculate the unknown values

if an increase in

That is, if

Then

In this case if

(1) We know that in inverse Proportion

In a problem, one pair would be given. So using the above equation, we can easily find the unknown terms

(2) We know that in inverse Proportion

xy= k

x=k/y

So we can find value of k from known values, and then use the formula to calculate the unknown values

If 20 workers can build a wall in 48 hours, how many workers will be required to do the same work in 30 hours?

Let the number of workers employed to build the wall in 30 hours be

We have the following table.

Number of Hours |
48 |
30 |

Number of workers |
20 |
y |

Obviously more the number of workers, faster will they build the wall.

So, the number of hours and number of workers vary in inverse proportion.

So 48 × 20 = 30 ×

So to finish the work in 30 hours, 32 workers are required

Following are the car parking charges near an Airport up to

2 hours Rs 60

6 hours Rs 100

12 hours Rs 140

24 hours Rs 180

Check if the parking charges are in direct proportion to the parking time.

We know that two quantities are in direct proportion if whenever the values of one quantity increase, then the value of another quantity increase in such a way that ratio of the quantities remains same

Here The charges are not increasing in direct proportion to the parking time because

2/60 ≠ 6/100 ≠ 12/140 ≠ 24/180

When two quantities

When two quantities

**Notes**-
**Ncert Solutions**

Class 8 Maths Class 8 Science