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 .
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 |
Cost of 6 mineral water bottles is Rs. 90. How many mineral water bottles can be bought for Rs. 225? | |||
Right Option : A | |||
View Explanation |
A dealer finds that 144 refined oil cans can be packed in 4 cartons of the same size. How many such cartons will he require to pack 896 cans? | |||
Right Option : B | |||
View Explanation |
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