header

GATE Online Mock Test Series (25 Tests) FREE For Limited Time         Attempt Free Tests at GyanPal.com

Electronics and Communication GATE test series

RATIO & PROPORTION: INTRODUCTION

ABOUT THE PAGE


PageInfo


This is the aptitude questions and answers section on "Ratios and Proportion " with detailed explanation for various interview, competitive examination and entrance test. Problems of three difficulty levels are given with detailed solution description, explanation, so that it becomes easy to grasp the fundamentals.

Browse Topics

Ratio:


A ratio is simply a fraction.   The following notations all express the ratio of x to y
=>  $x : y$ , $ x ÷ y$ , or $x/y$.
In the ratio x : y, we call a as the first term or antecedent and b, the second term or consequent.

Writing two numbers as a ratio provides a convenient way to compare their sizes.   For example, since $3/π < 1$, we know that 3 is less than π. 

A ratio compares two numbers.  Just as you cannot compare apples and oranges, so the numbers you are comparing must have the same units.  

For example, you cannot form the ratio of 2 feet to 4 meters because the two numbers are expressed in different units—feet vs. meters.

Top

Example 1: What is the ratio of 2 feet to 4 yards?

(A)  1 : 2        (B)  1 : 8          (C)  1 : 7        (D)  1 : 6            (E)  1 : 5        

The ratio cannot be formed until the numbers are expressed in the same units.  Let’s turn the yards into feet.
Since there are 3 feet in a yard, 4 yards = 4 * 3 feet = 12 feet . 
Forming the ratio yields $\text"2 feet"/\text"12 feet" = 1/6 $ or $1 : 6$
The answer is (D).

Note. Taking the reciprocal of a fraction usually changes its size.  For example,
$3/4 ≠ 4/3$
So order is important in a ratio=> 3:4 ≠  4:3.

Rule: The multiplication or division of each term of a ratio by the same non-zero number does not affect the ratio.

Ex. 4 : 5 = 8 : 10 = 12 : 15.
Also, 4 : 6 = 2 : 3.

Top

Proportion:


The equality of two ratios (fractions) is called proportion. If a : b = c : d, we write a : b :: c : d and we say that a, b, c, d are in proportion.

Here a and d are called extremes, while b and c are called mean terms.

$$\text"Product of means = Product of extremes"$$
Thus, $$a : b :: c : d ⇔ (b * c)= (a * d)$$

Top

Fourth Proportional:

If a : b = c : d, then d is called the fourth proportional to a, b, c.

Top

Third Proportional:

a : b = c : d, then c is called the third proportional to a and b.

Mean Proportional:

Mean proportional between a and b is ab.

Top

Comparison of Ratios:

We say that $(a : b) > (c : d) ⇔ a/b > c/d$

Top

Compounded Ratio:

The compounded ratio of the ratios: $(a : b), (c : d), (e : f) is (ace : bdf)$

Top

Duplicate Ratios:

Duplicate ratio of $(a : b)$ is $(a^2 : b^2)$

Sub-duplicate ratio of $ (a : b)$ is $(a^{1/2} : b^{1/2})$

Triplicate ratio of $(a : b)$ is $(a^3 : b^3)$

Sub-triplicate ratio of $(a : b)$ is $(a^{1/3} : b^{1/3})$

If $a/b = c/d$ then, ${a + b}/{a - b} = {c + d}/{c – d}$ [Componendo and Dividendo]

Top

Variations:


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, $x  ∝ 1/y$

Top