Ratio and Proportion:

Ratio compares two or more things of same kind.

If the two quantities are a and b, then ratio of a and b represented as a : b or (a / b)

Here a is called antecedent and b is called consequent

Types of ratios:

1. Duplicate ratio: This indicates ratio of the squares of two numbers.

Example: Duplicate ratio of 1 : 2 is 2 : 4

2. Sub-duplicate ratio: This indicates ratio of the square root of two numbers.

Ex: Sub-duplicate ratio of 9 : 16 is 3 : 4

3. Triplicate ratio: This indicates ratio of the cubes of two numbers.

Ex: Triplicate ratio of 2 : 4 is 8 : 64

4. Sub-triplicate ratio: This indicates ratio of the cube roots of two numbers.

Example: Sub-triplicate ratio of 8 : 64 is 2 : 4

5. Compound ratio: compound ratio is obtained by multiplying antecedent with antecedent and consequent with consequent.

Ex: compound ratio of A : B and C : D is AC : BD

6. Inverse ratio: When we replace the antecedent with consequent and consequent with antecedent then we get inverse ratio.

Ex: Inverse ratio of X : Y is Y : X

Previous year solved Questions:

1. Kiran obtained 12 marks more than that of Ashok. If the ratio of their marks is 3 : 4, find the sum of their marks?

A) 96 B) 72 C) 84 D) 108 E) None of these

Ans: C

Solution: Assume marks of Kiran = 3x

Marks of Ashok = 4x

According to the question, 4x – 3x = 12 => x = 12

=> Sum of their marks = 4x + 3x = 7x

=> Sum of their marks = 7 * 12 = 84

2. Sai and Naveen have invested in the ratio of 4 : 7. If both invested a total amount of Rs. 49500, then find the investment of Naveen?

A) 31500/- B) 1800/- C)31000/- D) 18500/- E) None of these

Ans: A

Solution:As per given data,

=> Investment of Naveen = (7 / 11) * 49500 = 31500

3. The speeds of three cars are in the ratio of 2 : 3 : 4 find the ratio between the time taken by these cars to cover the same distance.

A) 2 : 3 : 4 B) 4 : 3 : 2 C) 4 : 3 : 6 D) 6 : 4 : 3 E) None of these

Ans: D

Solution: Ratio of speed of three cars = 2 : 3 : 4

=> Ratio of time taken by these three cars = (1 / 2) : (1 / 3) : (1 / 4) = 6 : 4 : 3