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Ratio and Proportion Questions and Answers with clear explanation for IBPS Clerk, IBPS PO, SBI PO, SBI Clerk, RRB, RBI, SSC & other competitive exams. Aspirants can practice Ratio and Proportion test questions and answers on a daily basis to improve your problem solving skill. Ratio and Proportion is most important for competitive exams conducting by the employers/Exam board every year. IBPS Guide provides you lots of fully solved Ratio and Proportion questions and answers with explanation. We provide Ratio and Proportion quiz on a daily basis to increase your performance in exam.

**Introduction:**

Ratio is a comparison of two quantities by division. Ratio represents the relation that one quantity bears to the other. It is represented as a:b. In any ratio a:b, a is called Antecedent and B is called Consequent. It is an abstract (without units) quantity.

A ratio remains unaltered if its numerator and denominator are multiplied or divided by the same number, e.g. 4:3 is the same as the (4 x 10) : (3 x 10) ie 40:30.

**Different Types of Ratios:**

**Duplicate Ratio: **a^{2} : b^{2} is called duplicate ratio of a : b.

**Triplicate Ratio: **a^{3} : b^{3} is called triplicate ratio of a : b.

**Sub – Duplicate Ratio:** √a :√b is called sub-duplicate ratio of a : b.

**Sub – Triplicate Ratio: **^{3}√a :^{3}√b is called sub-triplicate ratio of a : b

**Compound Ratio: **ab : cd is the compound ratio of a : c and b : d. It is the ratio of the product of the antecedents to that of the consequents of two or more given ratios.

**Inverse Ratio: **1/a : 1/b is the inverse ratio of a : b.

**Componendo and Dividendo:** If a/b = c/d, then (a + b)/(a – b) = (c + d)/(c – d)

**Proportion:**

Proportion is a statement that two ratios are similar. When two ratios are equal, they make a proportion, i.e. if a/b = c/d, then a, b, c and d are in proportion. This is represented as a:b :: c:d. When a, b, c and d are in proportion, then a and d are called the Extremes and b and c are called the Means, also Product of the Means = Product of the Extremes i.e. bc = ad.

**Continued Proportion: **If these quantities a, b and c are such that a:b :: b:c, then b^{2} = ac and a, b and c are in continued proportion. Also the quantity c is called the third proportion of a and b.

**Fourth Proportion:** If four quantities a, b, c and x are such that a:b :: c:x, then ax = bc and x is called the fourth proportion of a, b and c.

**Mean or second Proportion:** If three quantities a, b and x are such that a:x ::x:b, then x^{2} = ab and x is called the mean of a and b. Also, if a:b = c:d, then the following properties holds good.

**i) **b:a = d:c (Invertendo)

**ii) **a:c = b:d (Alternendo)

**iii) **(a + b) : b = (c + d) : d (Componendo)

**iv) **(a – b) : b = (c – d) : d (Divendendo)

**v) **(a + b)/(a – b) = (c + d)/(c – d) (Componendo – Divendendo)

**Variation: **

If two quantities x and y are related in such a way that as the quantity x changes it also brings a change in the second quantity y, then the two quantities are in variation.

**Direct Variation: **The quantity x is in direct variation to y, if an increase in x makes y to increase proportionally. Also decrease in x makes y to decrease proportionally it can be expressed as x = ky, where k is called the constant of proportionality.

**Eg:** Cost is directly proportional to the number of articles bought.

**Inverse Variation: **The quantity x is in inverse variation to y, if an increase in x makes y to decrease proportionally. Also a decrease in x makes y to increase proportionally. It can be expressed as x = k/y, where k is a constant of proportionality.

**Eg:** The time taken by a vehicle in covering a certain distance is inversely proportional to the speed of the vehicle.

**Joint Variation: **If there are more than two quantities x, y and z and x varies with both y and z, then x is in joint variation to y and z. It can be expressed as kyz, where k is constant of proportionality.

**Eg:** Men doing a work in some number of days working certain hours a day.

**Distribution of Amount: **If an amount A is distributed in the ratio a:b, then

**First part =**a/(a+b) x A; **Second Part =**b/(a + b) x A

**Formulae: **

**1)** If a:b :: b:c, then a/b = b/c => c = b^{2}/a

**2)** If a:b :: c:d, then a/b = c/d => d = bc/a

**3) **If a:x :: x:b, then x = √ab (x is mean proportional)

**4) **If x/y = 1, then (x + a)/(y + a) = 1 and (x – a)/(y – a) = 1

**5) **If x/y > 1, then (x + a)/(y + a) < x/y and (x –a)/(y – a) > x/y

**6) **If x/y < 1, then (x + a)/(y + a) > x/y and (x –a)/(y – a)< x/y

**7) **If a/b = c/d = e/f = …………… = k (constant), then (a + c + e + ……..)/(b + d + f + ……..) = k