Direct Variation
Direct Variation
If two quantities are linked in such a way that an increase in one quantity leads to a corresponding increase in the other and vice-versa,then such a variation is called a direct variation. If two quantities are in direct variation ,then we also say that they are proportional to each other .
Illustration: If the cost of 93 m of a certain kind of plastic sheet Rs 1395, then what would it cost to buy 105 m of such plastic sheet?
Solution: Let the cost of plastic sheet 105m is x
| Plastic Sheet (m) | 93 | 105 |
| Cost of Sheet (Rs) | 1395 | x |
According to Direct Variation:
On solving as these numbers we see that 1395 is divisible by 93.
x = 1575 Rs
Illustration: In which of the following tables,a and b vary directly. Also ,find the constant of variation if a and b are in direct variation .
(i)
| a | 4 | 7 | 21 | 28 |
| b | 12 | 21 | 63 | 84 |
(ii)
| a | 2.5 | 5 | 7.5 | 10 | 15 |
| b | 10 | 20 | 30 | 40 | 60 |
(iii)
| a | 1 | 2 | 3 | 4 | 5 |
| b | 2 | 1 | 6 | 3 | 2/5 |
Solution:
(i) We have,
Thus, the ratio of the corresponding values of a and b is constant
.
Hence, a and b are in direct variation with the constant of variation equal to 1/3
(ii) We have,
.
This shows that the ratio of the corresponding values of a and b is constant and is equal to .Thus, a and b vary directly. The constant of variation is
(iii) It is evident from the table that the ratio of the corresponding values of a and b is not constant. So, a and b are not in direct variation i.e they do not vary directly .
A motor boat covers 550 km in 5 hrs. What distance will it cover in 8 hrs (speed remaining the same)?
| |||
| Right Option : C | |||
| View Explanation | |||
A motor bike travels 420 km on 20 litres of petrol. How far would it travel on 9 liters of petrol? | |||
| Right Option : A | |||
| View Explanation | |||
The cost of 5 kg of sugar is Rs. 105. What will be the cost of 15 kg of sugar? | |||
| Right Option : B | |||
| View Explanation | |||
Students / Parents Reviews [20]
About Abhyas metholodology the teachers are very nice and hardworking toward students.The Centre Head Mrs Anu Sethi is also a brilliant teacher.Abhyas has taught me how to overcome problems and has always taken my doubts and suppoeted me.
Shreya Shrivastava
8thMy experience with Abhyas is very good. I have learnt many things here like vedic maths and reasoning also. Teachers here first take our doubts and then there are assignments to verify our weak points.
Shivam Rana
7thThird consective year,my ward is in Abhyas with nice experience of admin and transport support.Educational standard of the institute recumbent at satisfactory level. One thing would live to bring in notice that last year study books was distributed after half of the session was over,though study ...
Ayan Ghosh
8thMy experience with Abhyas academy is very good. I did not think that my every subject coming here will be so strong. The main thing is that the online tests had made me learn here more things.
Hiya Gupta
8thBeing a parent, I saw my daughter improvement in her studies by seeing a good result in all day to day compititive exam TMO, NSO, IEO etc and as well as studies. I have got a fruitful result from my daughter.
Prisha Gupta
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Yogansh Nyasi
7thIt was a good experience with Abhyas Academy. I even faced problems in starting but slowly and steadily overcomed. Especially reasoning classes helped me a lot.
Cheshta
10thAbhyas institute is one of the best coaching institute in the vicinity of Ambala cantt.The institute provides good and quality education to the students.The teachers are well experienced and are very helpful in solving the problems. The major advantages of the institute is extra classes for weak...
Shreya Shrivastava
8thMy experience with Abhyas Academy has been very good. When I was not in Abhyas whenever teacher ask questions I could not speak it confidently but when I came in Abhyas, my speaking skills developed and now I am the first one to give the answer of teachers question.
Upmanyu Sharma
7thIn terms of methodology I want to say that institute provides expert guidence and results oriented monitering supplements by requsite study material along with regular tests which help the students to improve their education skills.The techniques of providing education helps the students to asses...
Aman Kumar Shrivastava
10thUsually we see institutes offering objective based learning which usually causes a lag behind in subjective examinations which is the pattern followed by schools. I think it is really a work of planning to make us students grab the advantages of modes of examination, Objective Subjective and Onli...
Anika Saxena
8thOne of the best institutes to develope a child interest in studies.Provides SST and English knowledge also unlike other institutes. Teachers are co operative and friendly online tests andPPT develope practical knowledge also.
Aman Kumar Shrivastava
10thWe started with lot of hope that Abhyas will help in better understnding of complex topics of highers classes. we are not disappointed with the progress our child has made after attending Abhyas. Though need to mention that we expected a lot more. On a scale of 1-10, we would give may be 7.
Manya
8thAbhyas Methodology is very good. It is based on according to student and each child manages accordingly to its properly. Methodology has improved the abilities of students to shine them in future.
Manish Kumar
10thAbhyas is good institution and a innovative institute also. It is a good platform of beginners.Due to Abhyas,he has got knoweledge about reasoning and confidence.My son has improved his vocabulary because of Abhyas.Teacher have very friendly atmosphere also.
Manish Kumar
10thMy experience with Abhyas academy is very nice or it can be said wonderful. I have been studying here from seven class. I have been completing my journey of three years. I am tinking that I should join Abhyas Academy in tenth class as I am seeing much improvement in Maths and English
Hridey Preet
9thAbhyas institute is one of the best coaching institute in the vicinity of Ambala Cantt area. The teachers of the institute are well experienced and very helpful in solving the problems of the students.The good thing of the institute is that it is providing extra classes for the students who are w...
Aman Kumar Shrivastava
10thIt has a great methodology. Students here can get analysis to their test quickly.We can learn easily through PPTs and the testing methods are good. We know that where we have to practice
Barkha Arora
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Om Umang
10thThe experience was nice. I studied here for three years and saw a tremendous change in myself. I started liking subjects like English and SST which earlier I ran from. Extra knowledge gave me confidence to overcome competitive exams. One of the best institutes for secondary education.
