Ratio And Proportion
Definition of Ratio:
Comparison of two different quantities having the same units.
Types of Ratio:
Let us assume that, two numbers are ‘a’ and ‘b’.Then the ratio is a: b.
Therefore,
⦁ Duplicate ratio: a2: b2
⦁ Sub duplicate ratio:
⦁ Triplicate ratio: a3: b3
⦁ Sub triplicate ratio:
⦁ Inverse ratio:
⦁ If three different ratios are a: b, c : d and d: e
Compounded ratio:
Some important properties of ratio:
⦁ If in the ratio a/b, the numerator and the denominator are multiplied or divided by the same number then the value of the ratio remains the same.
Case 1: Multiplying numerator and denominator by same number x: Ratio = Thus, cancelling out x further results in the same ratio a/b.
Case 2: Dividing numerator and denominator by same number y: Ratio = Thus, cancelling out y further results in the same ratio a/b.
2. If p/q = r/s = t/u = v/w = m then m =
Comparison of two ratios: Suppose we have to compare two different ratios 12/17 and 13/11. Here to find which ratio is greater or lesser than the other, we use the cross multiplication method. Simply cross multiply the denominator to the numerator of another ratio.
(12×11) (13×17) = 132 221 Comparing we get 132 < 221 thus.
Proportion: If two ratios are equal then the 4 terms are called proportion. For example: = It can also be written as: a : b:: c : d Here terms a and d are called extremes and terms c and d are called means.
Types of Proportion: If the ratio is a: b
⦁ Mean proportion:
⦁ Third proportion:
⦁ If three numbers a, b and c are given then
Fourth proportion:
Note:
⦁ If a: b = 2 : 3 and b: c = 4: 5 Then
⦁ If a : b = 1 : 2, b : c = 3 : 4 and c : d = 2 : 3
⇒ a : b : c : d = 6 : 12 : 16 : 24
Example 1: If 2a = 3b = 4c = 5d then find a : b : c : d.
Solution:
2a = 3b = 4c = 5d = (60) = LCM of (2,3,4,5)
⇒ a : b : c : d = 30 : 20 : 15 : 12
Example 2: If a : (b + c) = 1 : 2 and b : (c + a) = 3 : 4 then find c : (a + b).
Solution:
In first case: a + (b + c) = 1 + 2 = 3
In second case: b + (c + a) = 3 + 4 = 7
Now multiplying first equation with 7 and Second equation with 3: a : (b + c) = 7 : 14 and b : (c + a) = 9 : 12 Thus, by comparison:
a = 7 b = 9
So, c = 21 – (7 + 9) = 5
Thus, c : (a + b) = 5 : 16
Download PDF for Formula Sheets: Ratio And Proportion
Check Out:
- Previous Year's Papers for CSIR-NET Exam: Attempt Here
- Study Notes for Part A: General Aptitude - Download PDF Here
- Study Notes for CSIR-NET Chemical Science - Download PDF Here
- Study Notes for CSIR-NET Life Science - Download PDF Here
More from us:
Get Unlimited access to Structured Live Courses and Mock Tests - Online Classroom Program
Get Unlimited Access to CSIR NET Test Series
~ We hope you understood the above article. Kindly UPVOTE this article and Share it with your friends.
Stay Tuned for More Such Articles !!
BYJU'S Exam Prep Team
Download the BYJU’S Exam Prep App Now.
The Most Comprehensive Exam Prep App.
#DreamStriveSucceed
App Link: https://bit.ly/3sxBCsm
Comments
write a comment