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& testbook.com, , Ratio and Proportion: Concepts, Solved Examples, &, Preparation Strategies, 2021/04/21, , Ratios refer to the quantitative relation between two numbers or amounts or quantities. It shows the, number of times one value contains the other value or is contained within the other value. On the other, , hand, a proportion simply implies that one ratio is equal to the other., , In this article, we are going to cover the key concepts of Ratio and Proportion along with the various, types of questions, types of proportion, tips and tricks, ratio and proportion formula, etc. We have also, added a few solved examples, which candidates will find beneficial in their exam preparation. Read the, , article thoroughly to clear all the doubts regarding the same., , If you’ve learned Ration and Proportion, you can move on to Profit and Loss concepts., , What are Ratio and Proportion?, , The idea of ratio and proportion is primarily based on ratios and fractions. This topic is kind of a key, foundation for various other topics in mathematics. We had a brief intro to ratios and proportions where, we read that ratios are used for comparing two quantities of an identical style. Whereas when two or, more such ratios are identical, they are declared to be in proportion. Now let us read and understand, them in detail., , What is Ratio?, , Ratios are used when we are required to express one number as a fraction of another. If we have two, quantities, say x and y, then the ratio of x to y is calculated as x/y and is written as x:y. The first term of, , the ratio is called antecedent and the second term is called the consequent., , What is Proportion?, , Two identical ratios are definitely in proportion, this implies that proportion is an equation that specifies, , that the two given ratios are identical to one another., Or, , We can Say that the proportion states the equivalency of the two fractions or the ratios. Proportions are, represented by the symbol (: @ or equal to (=).
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That is the proportion is signified by double colons. For example, ratio 6:8 is the same as ratio 3:4. This, can be written as 6:8::3:4., , Product of means = Product of extremes, , Thus, a:b::c:d (bxc)=(axd), Types of Proportion, , Ratio and proportion find applications in solving many daily life problems for example while we are, comparing altitudes, weights, length, time or if we are negotiating with company transactions, also while, adding elements in cooking, and much more., , The proportion can further be categorised into:, , Direct Proportion, , Inverse Proportion, , Continued Proportion, , Direct Proportion, , In proportion, if two sets of given numerals are rising or falling in the same ratio, then the ratios are, considered to be directly proportional to each other. That is we can say that direct proportion illustrates, the relationship between two portions wherein the gains in one there is a growth in the other quantity, too. Likewise, if one quantity drops, the other also decreases., , Therefore, if “X” and “Y” are two quantities, then the direction proportion is composed as x«y., Inverse Proportion, , The inverse proportion as the name outlines this is in contrast to the direct one; where the relationship, between two quantities is defined such that growth in one leads to a decline in the other quantity., Likewise, if there is a drop in one portion, there is an expansion in the other portion., , Accordingly, the inverse proportion of two quantities, say “p” and “q” is represented by p«(1/q)., Continued Proportion, , If we assume two ratios to be p: g and r: s and we are interested in determining the continued proportion, for the given ratio. Then we transform the means to a single term/digit. That is we will find the LCM of, means., , For the provided ratio, the LCM of q & r will be qr., The next step is to multiply the first ratio by r and the second ratio by q as shown:, First ratio- rp: rq, , Second ratio- rq: qs
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Thus, the continued proportion can be documented in the form of rp: qr: qs, , Ratio and Proportion Formula, , Well acknowledged with the definition and various types let us now learn the formula regarding the, topic:, , Ratio Formula, , For any two given quantities say x and y, the formula for ratio is:, xy > x/y, Where, , x that is the first term is also called the antecedent., , y which is the second term is also called the consequent., , For instance, ratio 7: 17 is depicted by 7/17, where 7 is antecedent and 17 is consequent., , Proportion Formula, , Now for the proportion formula consider two ratios, p:q and r:s. Then, p:q:: r:s—p/q=r/s, , Here, the two terms g and r are named mean terms., Whereas the other two terms i.e. p ands are understood as extreme terms., , Difference Between Ratio and Proportion, , Both the concepts of ratio and proportion are essential parts of mathematics. Even in real life, we find, examples relating to the same such as the rate of speed given by the formula distance/time or price of, ride per meter (i.e rupees/meter) of the price of material w.r.t rupees, etc. Let us understand the, , difference between ratio and proportion with the below table:, , , , Ratio Proportion, , , , Ratios are applied to compare the size of two, items with an identical unit., , Proportions are applied to represent the link, between the two ratios., , , , A ratio is a form of expression., , Proportion depicts a form of an equation., , , , Ratios are represented with a colon (:), slash (/)., , Proportions are represented with a double colon, (::) or equal to the symbol (=)., , , , Example: x: y > x/y, , , , , , Example: p:q:: r:s—p/q=r/s
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Compounded Ratio, , If two or more ratios are given and the antecedent of one is multiplied with antecedent of others and, consequents are multiplied with consequences of others, then the ratio obtained is called compound, , ratio., , The compounded ratio of the ratios (a : b), (c : d), (e: f) will be (ace : bdf), , Various types of questions are asked from the proportion, Some of them are as follows., (a) Third Proportion, , Ifa: b=b:c, then cis called the third proportion to a and b., , (b) Fourth Proportion, , Ifa: b=c:d, then dis called the fourth proportion to a, b, c., , (c) Mean Proportion, , Mean proportion of a and b will be root over ab., , Once you've mastered Ratio and Proportion, Also, learn more about Simplification and approximation, , concepts in depth!, How to Solve Question Based on Ratio and Proportion- Know all Tips and Tricks, , Candidates can find different tips and tricks from below for solving the questions related to ratio and, , proportion., , Tip # 1: In ratio, if both the antecedent and the consequent are multiplied or divided by the same number, , (except 0) then the ratio will remain the same., , Tip # 2:If a proportion is such as a:x::x:b then x is called the mean proportional or second proportional of, , a and b. And if a proportion is such that a:b::b:x then x is called the third proportional of a and b., Tip #3: Componendo rule: If a/b = c/d then atb/b=c+d/d, , .Tip # 4: Dividendo rule: If a/b = c/d then a-b/ b= c-d/d, , Tip #5: Componendo & Dividendo rule: If a/b = c/d then a+b / a-b = c+d/c-d, , Tip # 6: Invertendo rule: If a/b = c/d then b/a = d/c, , Tip #7: Alternendo rule: If a/b = c/d then a/c = b/d, , Also check Problem on Ages concepts here once you are through with Ratio and Proportion concepts!
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Ratio and Proportion Solved Sample Questions, , Question 1: If A: B= 2:3 andB:C=5:7 then what is the ratio A: B:C?, Solution: A: B=2:3B:C=5:7, , Multiply by 3/5 so as to make the ratio term of B Common, B: C =5 x 3/5:7 x 3/5, > B:C=3:21/5, , A. Bag= 2:3: 21/5, , =2*5:3%5:21/5x5, , Hence, A:B:C=10:15:21, , Question 2: What is the equivalent compound ratio of 17 : 23 ::115 : 153 ::18: 25, , Solution: We know, compound ratio of the ratios (a : b), (c : d), (e : f) will be (ace : bdf) Thus, the, compound ratio of (17 : 23), (115 : 153), (18 : 25) = (17 x 115 x 18) / (23 x 153 x 25)=2:5, , Question 3: If 3:27::5:?, , Solution: If 3: 27::5:?, , 3/27 =5/?, , 2=5 27/3, , ?=45, , Question 4: Find the mean proportional between 14 & 15?, Solution: As we know that, mean proportional = v(ab), , = v(14 « 15), , = 145, , So, the mean proportional of 14 and 15 = 14.5, , Question 5: Mean proportional of 4 and 36 is a and third proportional of 18 and a is b. Find the fourth, proportional of b, 12, 14., , Solution: Given,, Mean proportional of 4 and 36 =a, = a2=4% 36, , =a=12
