Study notes on Ratio and Proportion for DSSSB Exam

Dear Readers, 

Here we are providing you Study notes on Ration and Proportion which will be helpful for Upcoming CTET and DSSSB Exams


Ratio is used to compare the two quantities of same unit. If given quantities are not in same unit, Ratio of those quantities cannot be calculated. Commonly ratio is expressed in the form of fraction.

For example :- If A and B are two quantities of same unit then their ratio will be   or A : B.
where A is known as antecedent (1st term) and B is called consequent (2nd term).

Note:-  If each term of ratio is multiplied or divided by the same non - zero number, in that case ratio does not get affected. It remains same.
For example, 3 : 5 is the same as (3 x 2)/(5 x 2)=6/10 =3/5

Expression of Ratio in Percentage form:-
Ratio can be expressed as percentage. To express the value of a ratio as a percentage, we multiply the ratio by 100.
Example :-Convert ratio 3/5 in percentage form.
Solution:- (3/5) x 100=60 %

Types of Ratio:-
(1) Duplicate Ratio :- When both terms of a ratio are multiplied by themselves or squared, then resulted ratio is known as duplicate ratio. If a and b are two numbers then their ratio will be a : b and duplicate ratio will be a2 : b2.
Example :- Duplicate ratio of 8 : 9 = 82 : 92 = 64 : 81

(2) Sub-duplicate Ratio :- This is the ratio of square roots of two numbers. If two numbers are a and b, then sub-duplicate ratio between them will be √a : √b
Example :- Sub - duplicate ratio of 4 : 9 = √4 : √9 =2:3

(3) Triplicate Ratio :- The ratio of cubes of two numbers is known as triplicate ratio. If a and b are two numbers then their triplicate ratio will be a3 : b3.
Example :- Triplicate ratio of    3 : 4 = 33 : 43= 27 : 64

(4) Sub-triplicate Ratio :- The ratio of cube roots of two numbers is known as sub-triplicate ratio. If a and b are two numbers then sub-triplicate ratio of a and b will be

(5) Inverse Ratio :- Inverse Ratio of two numbers refers to the ratio of their reciprocal. If a and b are two numbers then the inverse ratio of a and b is (1/a): (1/b) =b:a
Example:- Inverse ratio of 3 and 4=(1/3): (1/4)=4:3

(6) Compound Ratio :- Compound ratio of two ratios refers to the ratio made after multiplying their antecedents and consequents. The compound ratio of a : b and c : d will be
a x c: b x d= ac:bd

Proportion:- The equality of two ratios is called proportion. If a, b, c and d are in proportion then we can write them
as a : b = c : d or a : b : : c : d.
In proportion, we call ‘first and fourth terms’ as extremes and ‘second and third terms’ as means.

Note :- In a proportion, product of extremes = product of means. If a : b : : c : d then ad = bc.

Types of Proportion:-

(1) Continued Proportion :- Four quantities a, b, c and d are said to be in a continued proportion, if
a :b =b:c=c:d
or (a/b) =(b/c) or b2=ac
In this relationship, b is said to be the mean proportional between ‘a and c’ and c is said to be a third proportional to ‘a and b’.

(2) Direct proportion:-
If A is directly proportional to B then as A increases, B also increases proportionally.

For example:- The relationship between speed, distance and time, is as follows - “speed is directly proportional to distance when time is constant”. It means if speed is doubled, distance travelled will also be doubled when time is kept constant.

(3) Inverse proportion:- A is inversely proportional to B means if A increases, B decreases proportionally.

For example:- If speed is doubled, time taken to cover the same distance is reduced to half.

Some properties on Ratio and Proportion:-

(1) Rule of Invertendo-
If a : b :: c : d, then b : a :: d : c

(2) Rule of Alternendo-
If a : b :: c : d, then a : c :: b : d

(3) Rule of Componendo-
If a : b :: c : d, then its componendo will be
(a+b) : b :: (c+d) : d.

(4) Rule of Dividendo-
If a : b :: c : d then (a-b) : b :: (c-d) : d.

(5) Rule of Componendo and Dividendo-
If a : b :: c : d, then its componendo and dividendo will be
=(a+b) : (a-b) :: (c+d) : (c-d)
(a+b)/ (a-b)  =(c+d)/ (c-d)

Some Memorable Points :-

(1) If a : b :: b : c, then c is called the 3rd proportional to a and b. c will be calculated as following :-
a : b :: b : c
a /b= b /c

(2) If a : b :: c : d, then d is called the 4th proportional to a, b and c. d will be calculated as following.
a : b :: c : d
a /b= c /d

(3) Mean proportional between a and b is  √ab
If mean proportional is ‘x; then
a /x= x /c

Enjoy free Video Lecture on Ratio and Proportion here:


Team clear ctet.


Want to know more

Please fill in the details below:



admit-card,10,Answer Key,4,answer-key,1,Child Development,39,Child Pedagogy,39,CLAT Coaching,1,CLAT Coaching Classes,1,CLAT Coaching Delhi,1,CTET,20,CTET Coaching,1,ctet coaching centre delhi,1,ctet coaching in delhi,1,ctet previous paper,1,ctet previous year solved paper,1,CTET Question Papers,1,CTET QUIZ,32,CTET-2017,1,Cut Off,5,DSSSB,58,DSSSB Coaching,6,DSSSB Exam,2,DSSSB Teachers,5,DSSSB Teachers Selection,1,Educational Psychology,5,Eligibility,1,English Grammar,3,English-Pedagogy,19,EVS Pedagogy,2,EVS-Pedagogy,6,EXAM,1,Exams,3,Featured,21,General Science-Biology,1,Guest Teachers,1,Hall Ticket,1,Hindi,3,Imp-Tips,4,job alerts,1,KVS,11,kvs online recruitment 2018,1,kvs teacher recruitment 2018,1,kvs tgt pgt recruitment 2018,1,Latest Article,6,Latest Articles,12,Latest-Articles,28,Mock test,33,MOCK TEST-DSSSB QUIZ,1,NCF,104,Notification,21,Notifications,1,PGT,2,PRT,4,Quant Notes,4,Question Paper,1,Reasoning,2,Religious-Social,1,Results,8,Revision of the Day,15,SST- Geography,12,SST-Civics and Economics,12,SST-History,27,Study Notes,38,Syllabus,18,Teachers Vacancies,2,TGT,1,Vacancy,1,
DSSSB, CTET & KVS Exam Preparation | Clear CTET: Study notes on Ratio and Proportion for DSSSB Exam
Study notes on Ratio and Proportion for DSSSB Exam
Follow the Study notes on Ration and Proportion for DSSSB Exam
DSSSB, CTET & KVS Exam Preparation | Clear CTET
Loaded All Posts Not found any posts VIEW ALL Readmore Reply Cancel reply Delete By Home PAGES POSTS View All RECOMMENDED FOR YOU LABEL ARCHIVE SEARCH ALL POSTS Not found any post match with your request Back Home Sunday Monday Tuesday Wednesday Thursday Friday Saturday Sun Mon Tue Wed Thu Fri Sat January February March April May June July August September October November December Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec just now 1 minute ago $$1$$ minutes ago 1 hour ago $$1$$ hours ago Yesterday $$1$$ days ago $$1$$ weeks ago more than 5 weeks ago Followers Follow THIS CONTENT IS PREMIUM Please share to unlock Copy All Code Select All Code All codes were copied to your clipboard Can not copy the codes / texts, please press [CTRL]+[C] (or CMD+C with Mac) to copy