Maths is a subject that needs lots of practice as it consists of difficult formulas which need to be memorized to solve the textbook problems. The Vedantu Concise Selina solutions of Class 10 maths are prepared according to the ICSE Class 10 Maths syllabus and solved by our subject experts. Practising the solutions will help the students to evaluate their performance and improve on their weak points.
Referring to these Selina Class 10 Chapter 7 Ratio and Proportion solutions while solving the textbook questions will help students to understand the concepts so that students can easily solve all the questions without any mistakes. All the solutions are provided by Vedantu in the simplest form for better understanding by the students.
The Vedantu solutions for Selina Concise Mathematics Class 10 Solutions chapter 7 - Ratio and Proportion are solved by our highly skilled subject experts accurately in a simple language so that students can easily understand it. It is framed according to the ICSE Class 10 syllabus and practising Selina Class 10 solutions regularly will make your concepts strong which in turn will help to fetch good marks. Solutions to chapter 7 Ratio and Proportion have been documented with diagrams wherever necessary.
We can say that the comparison of two quantities of the same kind by division is referred to as ratio.
The two numbers in a ratio can only be compared when they have the same unit. We make use of ratios to compare two things.
The ratio of any two same quantities p and q can be expressed as either p/q or p : q. Here p is referred to 'antecedent' and q is called 'consequent'.
There are various types of ratios in Maths they are as follows:
Compounded Ratio: The ratio of antecedent as product of antecedents of the ratios and consequent as product of consequents, then the ratio thus formed is called compounded ratio.
For example, the compound ratio of m : n and y : x is my : nx and that of a : b, c : d and e : f is the ratio ace : bdf.
Duplicate Ratio: The duplicate ratio is the copy of the given ratio. For example The duplicate ratio of the ratio a : b
= (a × a) : (b × b)
= a2 : b2
Reciprocal Ratio: The reciprocal ratio of a:b is the ratio (1/a):(1/b), where a≠0 and b≠0. Which can also be written as 1/a : 1/b = b: a. Hence reciprocal ratio is the inverse ratio of the previous ratio.
For example the reciprocal ratio of 2 : 3 is ½ : ⅓ = 3 : 2
Ratio of Equalities: If the antecedent and consequent are equal, the ratio is called ratio of equality, for example 5 : 5.
Ratio of Inequalities: If the antecedent and consequent are not equal, the ratio is called the ratio of inequality, for example 5:7.
The proportion is the relation between two ratios such as a : b :: c : d or a/b = c/d, where a,b,c, and d are integers. In simple words, proportion compares two ratios. When two ratios are equal, then they are said to be in proportion. Proportions are denoted by the symbol ‘::’ or ‘=’.
Suppose we have two numbers and we have to find the ratio of these two, then the formula for ratio is defined as;
p : q = p/q
where p and q are any two numbers, “p” is called the antecedent, and “q” is called the consequent.
For example given that the two ratios are p : q & r : s . The two terms ‘q’ and ‘r’ are called ‘means or mean term,’ whereas the terms ‘p’ and ‘s’ are known as ‘extremes or extreme terms.’
The following are the important properties of proportion used in solving problems related to ratio and proportions.
Addendo :
If m : n = o : p, then m + p : n + o
Subtrahendo :
If m : n = o : p, then m – p : n – o
Dividendo :
If m : n = o : p, then m – n : n = o – p : p
Componendo :
If m : n = o : p, then m + n : n = o + p : p
Alternendo :
If m : n = o : p, then m : o = n : p
Invertendo :
If m : n = o : p, then n : m = p : o
Componendo and Dividendo:
If m : n = o : p, then m + n : m – n = o + p : o – p
Let us learn some rules and tricks to solve problems based on ratio and proportion.
If u/v = x/y, then uy = vx
If u/v = x/y, then u/x = v/y
If u/v = x/y, then v/u = y/x
If u/v = x/y, then (u+v)/v = (x+y)/y
If u/v = x/y, then (u-v)/v = (x-y)/y
If u/v = x/y, then (u+v)/ (u-v) = (x+y)/(x-y), which is known as componendo -Dividendo Rule
If a/(b+c) = b/(c+a) = c/(a+b) and a+b+ c ≠0, then a =b = c
By referring to Vedantu Solutions, students can memorize the concepts behind the solutions very quickly. This will not only encourage students by giving them the confidence to answer all sorts of questions in the examinations but will also ensure that they learn the concepts in the long run as well. The Vedantu Selina Maths Chapter 7 Ratio and Proportion Solutions Class 10 focuses on answering the questions in the right way to encourage students to fetch full marks in the examination.
Vedantu Selina ICSE Chapter 7 Ratio and Proportion Solutions for Class 10 all questions are answered and explained by expert teachers as per ICSE board guidelines. By studying these Selina ICSE Solutions for Class 10 you can easily get high marks in ICSE Class 10 Board Examinations.
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