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Ratio and Proportion Problems | Methods, Aptitude Ques & Ans – Shortcut Tricks

Ratio And Proportion Problems

Candidates if you are planning to appear in any competitive exam then shortcut tricks for Ratio And Proportion Problems can be really helpful for you. It is necessary for all the students to gain the basic knowledge and methods to solve the problems. Candidates you are also provided with question and answers on the below section of this page. You can use these basic formulas to solve these questions and get ready for the aptitude test in the competitive exam. Using the below given formulas you will be able to solve the questions within few seconds and it may also help you in maintaining the speed. Aspirants you all are advised to have a glance on the below given formulas to solve Ratio and Proportion Problems.

In every competitive exams of the government sector, the exam pattern has one section named as aptitude test. This test is conducted to check our ability of solving the questions with a good speed. So candidates it is must for you all to know the tricks to solve the questions which you can get on this page which is well planned and structured by the team of www.recruitmentinboxx.com. Aspirants you can look down on some below listed Ratio And Proportion Problems and solve them.

Ratio And Proportion Problems

How To Solve Ratio And Proportion:

Before you go further and learn some easy tricks to solve the Ration and Proportion you must know about what is ratio? Ratio helps us to know about the relationship of two numbers. It let us know the proportion of how many times first number enclose the second number. Ratios are useful when you have to compare two quantities. You can use the below given method to solve the questions relates to ratios.

Proportion is a mathematical statement comparing two ratios. Two ratios are equal only when they are written fractional forms and the fractions should be equivalent. For solving the ratios or for finding whether the fractions are equivalent or not, you can use cross multiplication method. Below given are some easy and shortcut tricks to solve the problems related to ration and proportions.

Ratio and Proportion – Important Basic Formulas:


The ratio of two quantities a and b in the same units, is the fraction  and we write it as a : b.

In the ratio a : b, we call a as the first term or antecedent and b, the second term or consequent.

Eg. The ratio 5 : 9 represents5with antecedent = 5, consequent = 9.

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

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


The equality of two ratios 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.

Product of means = Product of extremes.

Thus, a : b :: c : d  (b x c) = (a x d).

Fourth Proportional

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

Third Proportional:

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

Comparison of Ratios

We say that (a : b) > (c : d)     a>c.bd

Compounded Ratio

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

Duplicate Ratios

Duplicate ratio of (a : b) is (a2 : b2).

Sub-duplicate ratio of (a : b) is (a : b).

Triplicate ratio of (a : b) is (a3 : b3).

Sub-triplicate ratio of (a : b) is (a1/3 : b1/3).

Ifa=c, thena + b=c + d [componendo and dividendo]
bda – bc – d


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, x1

Also Know About:

Permutation and Combination Formula, Aptitude Questions, Problems And Solutions

Anupat And Samanupat Question In Hindi:

Question 1: अनुपात 3:5 के वर्गानुपात और 5:4 के घनानुपात का मिश्र अनुपात ज्ञात कीजिए

Answer: 45:64      

Question 2: दो संख्याओं का अनुपात 5:9 है । प्रत्येक संख्या में 9 जोड़ देने पर उनका अनुपात16:27 हो जाता है, तो दूसरी संख्या क्या होगी?

Answer: 99

Question 3: एक राशि अ,ब और स में क्रमश: 3:5:12 के अनुपात मे विभाजित की जाती है। यदि अ और ब दोनो के कुल शेयर स से 800 रू. कम है, तो इनमें अ के कितने शेयर है?

Answer: 600 रू0

Question 4: यदि एक संख्या का चार पंचमांश दूसरी संख्या के 60% के समान है, पहली और दूसरी संख्या के बीच क्रमश: अनुपात क्या है?

Answer: 3:4

Question 5: एक कक्षा में लड़कों की संख्या लड़कियों की संख्या से 12 प्रतिशत अधिक है, तो लड़कों का लड़कियों से अनुपात क्या होगा?

Answer: 28:25

Question 6: तीन संख्याएँ 1/2:2/3:3/4 के अनुपात में है। सबसे बड़ी और सबसे छोटी संख्याओं का अन्तर 36 है। वे संख्याएँ है

Answer: 72,96,108

Question 7: A,B और C के वेतन का अनुपात क्रमश: 2:3:5 है। यदि उनके वेतन में क्रमश:15%, 10% और 20% की वृद्धि हुई,तो वेतन का नया अनुपात क्रमश: क्या होगा?

Answer: 23:33:60

Question 8: 38 और 15का तृतीयानुपाती है ?

Answer: 15*15/38   

Question 9: यदि a/b =7/9 और b/c=3/5 है तो a:b:c बराबर है ?

Answer: 7:9:15

Question 10: 6:7 के प्रत्येक पद में से छोटी से छोटी कौन-सी पूर्ण संख्या घटाई जाए कि नए पदों का अनुपात 16:21 से कम हो ?

Answer: 3     

Check Out: Compound Interest Formula – Monthly/Quarterly/Half Yearly With Example

Here, we have given all the questions to solve Ratio and Proportion Questions for Bank Po. Contenders will become able to solve Problems for Bank Exams by reading this page. Students who are preparing for any bank exam or any school exam. Here, on this page, we have provided Ratio and Proportion Class 6 to Ratio and Proportion Class 7 and for others. Candidates may read our page and clear all Ratio and Proportion Concept and Ratio And Proportion Basics.

Aspirants who have wished to get Ratio and Proportion in Hindi, for their suitability, we have provided Ratio and Proportion Word Problems in Hindi also and you may download Ratio And Proportion Pdf also by going through links available here. Individuals may analyze their knowledge by giving Ratio and Proportion Online Test and by solving Questions by applying Formula. Ratio and Proportion Aptitude test will help a lot to understand How to Solve Ratio and Proportion problems with Ratio and Proportion Sums.

Do You Know: How to Prepare For Maths Exam

Sample Worksheet:

Question 1: A and B together have Rs. 1210. If  of A’s amount is equal to  of B’s amount, how much amount does B have?

Answer: Rs. 484

Question 2: Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is:

Answer: 4 : 5

Question 3: A sum of money is to be distributed among A, B, C, D in the proportion of 5 : 2 : 4 : 3. If C gets Rs. 1000 more than D, what is B’s share?

Answer: Rs. 2000

Question 4:  Seats for Mathematics, Physics and Biology in a school are in the ratio 5 : 7 : 8. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the ratio of increased seats?

Answer: 2:3:4

START NOW: Logical Reasoning Test

Question 5: In a mixture 60 litres, the ratio of milk and water 2 : 1. If this ratio is to be 1 : 2, then the quanity of water to be further added is:

Answer: 40 litres

Question 6: What number has a 5:1 ratio to the number 10?

Answer: 50

Question 7: The inverse ratio of 3: 2: 1 is?

Answer: 2:3:6

Question 8: If a: b = 3:4, b:c = 7:9, c:d = 5:7, find a:d?

Answer: 5:12

Must Read This: How to Reduce Negative Marking In Exam

Question 9: The fourth proportional to 12, 14 and 18 is?

Answer: 21

Question 10: The mean proportional between 4 and 9 is?

Answer: 6

Question 10: In a certain room, there are 28 women and 21 men. What is the ratio of men to women? What is the ratio of women to the total number of people?

Answer: 4 : 7 

Question 11: In a group, the ratio of doctors to lawyers is 5:4. If the total number of people in the group is 72, what is the number of lawyers in the group?

Answer: 32

Question 12: In a bag, there are a certain number of toy-blocks with alphabets A, B, C and D written on them. The ratio of blocks A:B:C:D is in the ratio 4:7:3:1. If the number of ‘A’ blocks is 50 more than the number of ‘C’ blocks, what is the number of ‘B’ blocks?

Answer: 350

Question 13: If the ratio of chocolates to ice-cream cones in a box is 5:8 and the number of chocolates is 30, find the number of ice-cream cones.

Answer: 6

Question 14: In a mixture of 45 litres, the ratio of sugar solution to salt solution is 1:2. What is the amount of sugar solution to be added if the ratio has to be 2:1?

Answer: 2:1 

Question 15: A certain recipe calls for 3kgs of sugar for every 6 kgs of flour. If 60kgs of this sweet has to be prepared, how much sugar is required?

Answer: 20 kgs

Question 16: If a 60 ml of water contains 12% of chlorine, how much water must be added in order to create a 8% chlorine solution?

Answer: 30 ml

Question 17: There is a 20 litres of a solution which has 20% of bleach. Extra bleach is added to it to make it to 50% bleach solution. How much water has to be added further to bring it back to 20% bleach solution?

Answer: 48 litres

Question 18: 1 kg of cashews costs Rs. 100 and 1 kg of walnuts costs Rs. 120. If a mixture of cashews and walnuts is sold at Rs. 105 per kg, then what fraction of the total mixture are walnuts?

Answer: 1/4

Question 19: What number has a 5:1 ratio to the number 10?

Answer: 5

Question 20: If a: b = 7: 5, b: c = 9: 11, find a: b: c?

Answer: 63: 45: 55

Candidates if you want to beat the competition then you must solve these questions and check your ability of how much you are prepared to appear in the competitive exams. Getr yourself prepared to appear in the exams.

So, dear aspirants, you may solve above given all questions and get ready for any competitive exam with full confidence. Now you are able to score qualified marks in this topic. But still, if you have any doubt or any query related to this topic then you may ask in below given comment box. Our experts will solve your problem related to this with best solution and suggest you more easy solutions.


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