### Quantitative Aptitude Topic of the day: Ratio and Proportion

Ratio is a fraction of two values. It can be represented in any of the following ways:

=> x/y, x : y , x÷y

- In ratio of the form x : y, x is called as the antecedent/first term and y is the consequent/second term.
- Generally, ratio is a handy way to compare two terms.
- For example : 4 / π > 1 , it is clear that 4 > π
- One thing that has to be remembered while comparing two numbers in a ratio is that they should be represented in same units. For example, if x is in meters and y in litres they cannot be compared by using ratio as they are expressed in different units – meters vs litres.

A proportion is the equality of two ratios/ fractions.

- If x : y = a : b, it can be written as x : y :: a : b and it is said that x, y, a, b are in proportion.
- Here x and b are called extremes, while y and a are called mean terms.
- Product of means=Product of extremes

Thus,

x :y :: a : b => (y∗a)=(x∗b) - If x : y=a : b

b is called the fourth proportional to x, y and a.

a is called the third proportional to x and y.

- Sub-duplicate: Sub-duplicate ratio of (a:b) is (a^1/2: b^1/2)
- Duplicate ratio of (a:b) is (a^2:b^2)
- Triplicate Ratio:Triplicate ratio of (a:b) is (a^3:b^3)
- Sub-triplicate Ratio: Sub-triplicate ratio of (a:b) is (a^1/3:b^1/3)
- If a/b=c/d then, a+b/a−b=c+d/c−d This is known as Componendo and Dividendo.
- We say that x is directly proportional to y, if x=ky for some constant k and we write, x∝y
- We say that x is inversely proportional to y, if xy=k for some constant k and we write, x∝1y

Attempt the following questions to check your level of preparedness for ratio proportion questions in competitive exams. You can answer the questions in comments section. Also make sure you checkout tomorrow’s (**September 10**) **Winner’s Curry** Lunch update for **solutions** to these questions along with the **formulae **used in **VIDEO** format by our **Subject Expert.**

**Question 1 : If A : B = 2 : 3, B : C = 4 : 5, and C : D = 6 : 7, then A : B : C : D is:**

A) 16 : 22 : 30 : 35

B) 16 : 24 : 15 : 35

C) 16 : 24 : 30 : 35

D) 18 : 24 : 30 : 35

**Question 2: Gold is 19 times as heavy as water and copper is 9 times as heavy as water. In what ratio should these be mixed to get an alloy 15 times as heavy as water?**

A) 1:01

B) 2:03

C) 1:02

D) 3:02

**Question 3: The ratio of ducks and frogs in a pond is 37 : 39 respectively. The average number of ducks and frogs in the pond is 152. What is the number of frogs in the pond?**

A) 148

B) 152

C) 156

D) 144

**Question 4: In a class, boys and girls are in ratio of 4:5. If 25% of boys and 20% of girls leave the class, then what is the new ratio of boys and girls?**

A) 1:01

B) 2:03

C) 3:04

D) 4:05

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