Ratio and Proportions - a few points

Ratios

Points to remember:

i) The order of terms in ratio is very important.

ii) The quantity of ration must be expressed in the same units.

iii) The ratio is unaltered if each term is multiplied or divided by the same number.

iv) When a certain quantity ‘q’ is divided in a given ratio a: b, the two parts are

          (aq)/ (a+b), (bq)/ (a+b)

v) If a:b and c:d are two ratios, then ac:bd is called the compounded ratio of the given ratios.

Proportion

The equality of the two ratios is called proportion. Suppose the two ratios a: b and c: d are equal i. e, a: b = c: d. then we can write

          a: b: : c: d

Here, a and d are called the extremes and b, c are called the means.

Rules

i)                   ad = bc or product of extremes = product of means.

ii)                In a: b:: c: d, d is fourth proportional to a, b and c.

iii)              If x is the third proportional to a and b then a: b: : b: x

iv)              Mean proportional between a and b is √(ab)

Other Properties

If a/b = c/ d or a: b: : c: d

i)                   (a+b)/ b= (c+d)/ d

ii)                (a-b)/ b= (c-d)/ d

iii)              (a+b)/ (a-b) = (c+d)/ (c-d)

iv)              (a/ b) = (c/ d) = (a+b)/ (c+d) = (ka+kb)/ (kc+kd)