Ratios and Proportions
a/b is the ratio of a to b; b is not 0.
When two ratios are equal, they are said to be in proportion.
If a/b = c/d and can be written as a: b: : c: d.
where "a" and "d" are called "extremes" and "c" and "b" the means.
For a, b, c, d to be in proportion the product of the extremes = the product of the means. i.e. ad = bc
Direct proportion: When a/b = k or a = kb then "a" is directly proportional to "b", where k is a constant.
Inverse proportion: When "a" and "b" are so related that ab = k, a constant, then "a" and "b" are said to be inversely proportional to each other.
If a sum of money S is divided in the ratio a : b : c then the three parts are
(i) S(a / a+b+c)
(ii) S(b / a+b+c)
(iii) S(c / a+b+c)
If a : b = m : n and b : c = p : q then a : b : c = mp : np : nq
If A and B are two partners investing in the ratio of m : n for the same period of time, then the ratio of profits is m : n
If the investment is in the ratio m : n and the period in the ratio p : q then the ratio of profits is mp : nq.
If m kg of one kind costing 'a" rupees/kg is mixed with "n" kg of another kind costing Rs.b/kg, then the price of the mixture is (ma + nb)/(m+n)
If "a" varies as "b", then a = kb, where "k" is called the constant of proportionality. (Direct variation).