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?
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
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
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