# Notes On Direct And Indirect Proportion Pdf

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- Direct & Inverse Proportions/Variations
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- CBSE Class 8 Maths Revision Notes Chapter 13 - Direct and Inverse Proportions

## Direct & Inverse Proportions/Variations

If you need sample questions based on direct and inverse proportion for practice, then you are at right place. If the values of two quantities depend on each other in such a way that a change in one result in a corresponding change in other, then the two quantities are called in variations. There are two types of variations as below. If we need to buy more pens, then we require more money to buy the pens.

Here, the number of pens and cost of money are in direct variation. If a school has more number of students, then the school is required more number of teachers to teach the students. Here, the number of students and the number of teachers are in direct variations.

If we need to travel less distance, then we require less time taken to complete the journey. Here, the the distance and the time taken are in direct variation. If we need to less number of books, then we require less money to buy the books.

Here, the number of books and the money are in direct variation. It means, x is proportional to y. In such a case, if y 1 and y 2 are two values of y corresponding to the values of x 1 and x 2 of x respectively, then. Here, the number of workers and time taken are in inverse variation. Here, the the time taken to complete the work and the number of employees are in inverse variation. Thus, if two quantities x and y are in inverse variations, then xy is constant.

A worker is paid Rs for 8 days work. If he works for 20 days, how much will he paid? Answer: Rs Sanjay bought 12 registers for Rs Find the cost of 8 registers. If 36 men can do a piece of work in 25 days, then in how many days will 15 men complete it?

Answer: 60 Days. By how much should its speed be increased so that it may take only 6 hours to finish the same journey? An overhead tank has two taps. One is working as inlet and other as an outlet. If the tank can be filled in 3 hours by the inlet tap and it can be finished by the outlet tap in 4 hours, then find the time required to fill the tank if both the taps are opened simultaneously.

Answer: 12 hours. Answer: 65 days. A contractor employed men to build a house in 60 days. After 12 days, he was joined by 70 more man.

In how many days will the remaining work be finished? Answer: 36 days. It takes her 20 minutes to reach the school. If she wants to reach her school in 15 minutes, what should be her average speed? Two pipes A and B can fill a tank in 36 hours and 45 hours respectively.

If both the pipes are opened simultaneously, how much time will be taken to fill the tank? A and B undertake to due to do a piece of work for Rs A alone can do it in 6 days while B alone can do it in 8 days with the help of C, they finish it in 3 days.

Find the share of each. What number must be added to each of the numbers 6, 15, 20 and 43 to make four numbers proportional? P and Q together can complete a job in 8 days and 16 days respectively.

They work on alternate days with Q starting the job. In how many days will the job be completed? A mixture containing alcohol and water in the ratio 3 : 2. If 4 lt of water is added to the mixture the ratio becomes 3 : 4. Find the quantity of water in the given mixture. If 30 men working 7 hours a day can do a piece of work in 18 days.

In how many days will 21 men working 8 hours a day, do the same work? By what fraction the number of days required for whole work will change? Find x. What number must be added to each of the numbers 10, 18, 22, 38 to get the numbers which are in proportion? If he takes 42 minutes in all, then what is the total distance? Sheetal has enough money to buy 75 machines worth Rs each. How many machine can she buy if she gets a discount of Rs. A job can be completed by P in 15 days and by Q in 10 days.

If they work on alternate days starting with P. If 12 boys earn Rs in 7 days, what will 15 days earn in 6 days? In a hostel of 50 girls, there are food provision for 40 days.

If 30 more girls join the hostel, how will these provision last? A and B together can do a task in t hours. Find t. A can do a piece of work in 25 days and b can finish it in 20 days. They work together for 5 days and then A goes away. In how many days will B finish the remaining work?

An employer reduces the number of employees in the ratio of 15 : 8 and increases their wages in the ratio 14 : In what ratio, the wages bill is increased or decreased? How long would A and B take separately to do the same work? A contractor undertakes to construct a road in 20 days and engages 12 workers. How many more workers should be now engage in order to finish the job in time?

Three taps A, B, C can fill a tank in 10 minutes, 15 minutes and 20 minutes respectively. In how many days can 6 men and 11 boys complete the work? In how many days can 20 men and 6 women do the same work? How many more men should be employed so that to complete the work in another 10 days?

In a school, the maximum strength of each class is In class, then total number of students is a multiple of 5. On a certain day, 4 boys were absent and the ratio of the numbers of the remaining boys to that of the girls was 5 : 4. Find the ratio of total boys to that of girls. Find the pass mark. Find the distance from his house to the office.

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Need for Concepts of Variation To find out the quantity of each item needed by Mohan or, the time taken by five students to complete the job, we need study some concepts of variation. We will study the following types of variation:. Inverse proportion Two quantities x and y are said to be in inverse proportion, if whenever the value of x increases or decreases , then the value of y decreases or increases in such a way that xy remains constant. The first way is named as direct variation whereas the second way is named as an inverse variation. Direct Proportion If two quantities are related in such a way that an increase in one leads to a corresponding proportional increase in the other, then such a variation is called direct variation.

When you start studying algebra, you will also study how two or more variables can relate to each other specifically. Note : Just because two variables have a direct relationship, the relationship may not necessarily be a causal relationship causation , meaning one variable directly affects the other. There may be another variable that affects both of the variables. For example, there may be a correlation between the number of people buying ice cream and the number of people buying shorts. People buying ice cream do not cause people to buy shorts, but most likely warm weather outside is causing both to happen. When two variables are related directly, the ratio of their values is always the same.

## CBSE Class 8 Maths Revision Notes Chapter 13 - Direct and Inverse Proportions

If you need sample questions based on direct and inverse proportion for practice, then you are at right place. If the values of two quantities depend on each other in such a way that a change in one result in a corresponding change in other, then the two quantities are called in variations. There are two types of variations as below.

Register Now. Hey there! We receieved your request. There are so many situations in our life where we see some direct or indirect relationship between two things.

In these lessons, we will learn how to solve direct proportions variations and inverse proportions inverse variations problems. The following diagram gives the steps to solve ratios and direct proportion word problems. Scroll down the page for examples and step-by-step solutions. Two values x and y are directly proportional to each other when the ratio x : y or is a constant i.

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