“Ratio and Proportion" is one of the easiest topics in quantitative section in IBPS. It is for this reason that questions from these topics are often asked in conjunction with other topics. The fundamentals of this topic are hence important not just from a stand-alone perspective, but also to answer questions from other topics.

Properties of Ratios
● A ratio need not be positive. However, if we are dealing with quantities of items, their ratios will be positive
● A ratio remains the same if both numerator and denominator are multiplied or divided by the same non-zero number, i.e.,
● $$\frac{a}{b} = \frac{pa}{pb} = \frac{qa}{qb} , p,q \neq 0$$
● $$\frac{a}{b} = \frac{a/p}{b/p} = \frac{a/q}{b/q} , p,q \neq 0$$

Properties of Proportions
If a:b = c:d is a proportion, then
● b:a = d:c
● c:d = a:b
● c:a = d:b
● Product of extremes = product of means i.e., ad = bc
● Denominator addition/subtraction: a:a+b = c:c+d , a:a-b = c:c-d
● a,b,c,d,.... are in continued proportion means, a:b = b:c = c:d = ....