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SSC Exam Quantitative Aptitude Study Material: A conceptual guide for Ratio and Proportions

Jun 22, 2016 14:32 IST

    SSC is well known for the recruitment of Group ‘B’ and ‘C’ posts under the Ministries/Departments in The Government of India. SSC organizes various examinations like Combined Graduate Level examination, Combine Higher Secondary Level, Stenographer and for SI/DP/CAPF, etc., throughout the year having almost the same Exam Pattern. The Exam paper is comprised of basically 4 subjects.

                  a. General Intelligence & Reasoning

                  b. English language & Comprehension

                  c. Quantitative Aptitude

                  d. General knowledge

    For more detail, click the link given below.

    SSC SI, CAPF & ASI Exam 2015: Exam Pattern

    SSC Combined Higher Secondary Level (10+2) Exam 2014: Exam Pattern

    SSC JHT & Hindi Pradhyapak and Sr. / Jr. Translators Exam 2014: Exam Scheme & Syllabus

    SSC Stenographer 2016: Take a look of Exam Pattern, Syllabus and Selection Procedure

    So, Jagranjosh.com has introduced a brief plan for revising topics at the time of examination. In this article, Ratio and Proportions which sometimes appear more difficult to understand in terms of  performing Hazzy calculations and complications. It clearly focuses on your logics and brain technicality.

    Ratio and Proportion is one of the basic concepts used widely in Quantitative Aptitude section. Concepts from ratios are used to solve questions in Averages, Profit & Loss, Data Interpretation etc.

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

    Compound Ratio: It is obtained by multiplying together the numerators for new numerator and denominators for new denominator.

    Example 1. If the ratios are 4:3, 15:20, 2:6 and 3:5 find the compound ratio?

    Duplicate ratio of a: b = a2 : b2

    Triplicate ratio of a: b = a3 : b3  etc.

    Example 2. If we divide 4185 into two parts such that they are in ratio 7:2, then find the values of both the parts?

    Sol 2. Let the actual variable be 7x and 2x.


    The ratio of first , second and third quantities is given by

                                   ac : bc : bd

    If the ratio between first and second quantity is a:b and third and fourth is c:d.


    Similarly, the ratio of first, second, third and fourth quantities is given by

                                 ace : bce : bde : bdf

    If the ratio between first and second quantity is a: b and third and fourth is c:d .


    Example 3. If Savita has Rs 1880. How much money does Ravina have if the ratio of money with savita and Rita is 15: 7 and that with Rita and Ravina 16: 7?



                                                                       Product of the extreme = Product of the means

    Direct proportion: - The two given quantities are so related that if one quantity increases (or decreases) then the other quantity also increases (or decreases).

    Example 1. If 5 pens cost Rs 10 then 15 pen cost?

    Sol 1. It is seen that if number of pens increases then cost also increases. So,


    Inverse proportion: - The two given quantities are so related that if one quantity increases (or decreases) then the other quantity also decreases (or increases).

    Example 2.If 10 men can do a work in 20 days then in how many days 20 men can do that work?

    Sol 2. Here if men increase then days should decrease, so this is a case of inverse proportion, so


    Rule of three: It Is the method of finding 4th term of a proportion if all the other three are given, if ratio is a:b :: c:d then ,


    Compound proportion: - Lets take an example to explain this.

    Example3. If 9 men can do a piece of work in 40 days of 10 hours each, how many men will it take to do 12 times the amount of work if they work for 30 days of 9 hours?

    Solution 3:

    Step 2.

             1. Compare days with men : to do the work in less days we will need more men , so it is the case of inverse proportion hence,

                                                                    30 : 40 :: 9 : required no. of men

             2. Compare hours  with men : to do the work in less hours we will need more men , so it is the case of inverse proportion hence,

                                                                     9  : 10 :: 9 : required no. of men

             3. Compare work  with men : to do the more work we will need more men , so it is the case of direct proportion hence,

    1. A certain amount was to be distributed among A, B and C in the ratio 2: 3: 4 respectively, but was erroneously distributed in the ratio 7: 2: 5 respectively. As a result of this, B got Rs 40 less. What is the amount?

    (1) Rs. 210      

    (2) Rs. 270      

    (3) Rs. 230      

    (4) Rs. 280      

    (5) None of these

    Ans: (1)

    2. Rs.73,689/- are divided between A and B in the ratio 4: 7. What is the difference between thrice the share of A and twice the share of B?

    (1) Rs. 36,699

    (2) Rs. 46,893

    (3) Rs. 20,097

    (4) Rs. 26,796

    (5) Rs. 13,398

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