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 .
An agent receives a commission of Rs. 73.00 on sales of Rs. 1000.00. The commission will be get on sales of Rs. 100.00 is ____________ . | |||
| Right Option : A | |||
| View Explanation | |||
Reema types 540 words during half an hour. How many words should she type in 6 minutes? | |||
| Right Option : B | |||
| View Explanation | |||
An agent receives a commission of Rs. 73.00 on sales of Rs. 1000.00 The commission he will get on sales of Rs. 100.00 is ______ . | |||
| Right Option : A | |||
| View Explanation | |||
Students / Parents Reviews [20]
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Ayan Ghosh
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10thIn 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...
