For example : find the cost of 5 kg or 8 kg of sugar. Study the following table.
Observe that as weight of sugar increases, cost also increases in such a manner that their ratio remains constant.
We say that x and y are in direct proportion, if `x / y = k `"or"` x = ky.`
If x and y are in direct proportion, we can write `x_1 / y_1 = x_2/y_2`
`[y_1,y_2` are values of y corresponding to the values `x_1,x_2` of x respectively]
Thus, variables increasing (or decreasing) together need not always be in direct proportion. For example:
(i) physical changes in human beings occur with time but not necessarily in a predetermined ratio.
(ii) changes in weight and height among individuals are not in any known proportion and
(iii) there is no direct relationship or ratio between the height of a tree and the number of leaves growing on its branches.
Shaalaa.com | Introdution
A machine in a soft drink factory fills 840 bottles in six hours. How many bottles will it fill in five hours?
A photograph of a bacteria enlarged 50,000 times attains a length of 5 cm. What is the actual length of the bacteria? If the photograph is enlarged 20,000 times only, what would be its enlarged length?
A 5 m 60 cm high vertical pole casts a shadow 3 m 20 cm long. Find at the same time the length of the shadow cast by another pole 10 m 50 cm high
A mixture of paint is prepared by mixing 1 part of red pigments with 8 parts of base. In the following table, find the parts of base that need to be added.
|Parts of red pigment||1||4||7||12||20|
|parts of base||8||...||...||...||...|
A loaded truck travels 14 km in 25 minutes. If the speed remains the same, how far can it travel in 5 hours?
A 5 m 60 cm high vertical pole casts a shadow 3 m 20 cm long. Find at the same time the height of a pole which casts a shadow 5 m long.
Following are the car parking charges near a railway station up to
4 hours Rs 60
8 hours Rs 100
12 hours Rs 140
24 hours Rs 180
Check if the parking charges are in direct proportion to the parking time.