11. Ratio, proportion and variation. (time-work Speed)
11. Ratio, proportion and variation. (time-work Speed) |
(A) Ratio :
1. Ratio is a relation obtained by comparing two quantities of the same kind.
- The sign ‘ : ' is used to express ratio.
2. While finding a ratio between any two quantities, the two quantities must be of the same kind and expressed in the same units.
• The ratio has no units. It is a pure number.
e.g. find the ratio of 15 seconds to 2 minutes.
2 minutes= 2 x 60 seconds = 120 seconds.
The required ratio = 15 seconds ⁄ 120 seconds
= 1 ⁄ 8
i.e. 1:8.
3. For two non-zero numbers a and b, the ratio of a to b is written as a ⁄ b or a : b. This is read as ‘a is to b.
4. When two or more ratios, reduced to their lowest terms, are equal, they are called equivalent ratios.
(B) Proportion :
1. If a, b, c, d are four non-zero numbers such that a ⁄ b = c ⁄ d then the numbers a, b, c, d are said to be in proportion.
2. If a, b, c, d are in proportion, then a is called the first proportional; b, the second proportional; c, the third proportional and d, the fourth proportional.
3. If a, b, c, d are in proportion, then a and d are called the extremes; b and c are called the means.
Product of the extremes = Product of the means,
i.e. a × d = b × c.
(C) Variation :
♦ If one quantity changes with the change in the related quantity, the change is called a variation.
1. Direct variation :
When two interdependent quantities change in such a way that their ratio remains constant, then it is an example of direct variation.
e.g. the cost of mangoes varies directly as the number of mangoes.
If 2 mangoes cost Rs. 50, then 5 mangoes will cost Rs.125.
2. Inverse variation :
When two interdependent quantities change in such a way that their product remains constant, then it is an example of inverse variation.
e.g. if 6 persons finish a piece of work in 8 days, then 12 persons will finish the same work in 4 days. Here, the number of days varies inversely as the number of persons.
Post a Comment