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 car covers a distance of 300km in 4 hours. What distance will it cover in 7 hours? | |||
| Right Option : D | |||
| View Explanation | |||
5 bags of rice weigh 150 kg. How many such bags of rice will weigh 900 kg? | |||
| Right Option : D | |||
| 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 | |||
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10thAbhyas 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...
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